Simulation and Relationship Strength: Characteristics of Knowledge Flows Among Subjects in a Regional Innovation System

Abstract

A small-world simulation model of a regional innovation system combining the strength of the intersubject relationship of the regional innovation system with the loosely coupled system is constructed. We use a simulation to observe knowledge flow within the regional innovation system under relationships of varying strength. The results show that when the relationship between the subjects of the regional innovation system reaches a certain strength, the system will exhibit high module independence and high network integrity, forming a loosely coupled system. The knowledge flow in the system exhibits the emergence of a fast flow rate, a high mean value and little variance. When relationship strength is at other levels, the emergence of knowledge cannot be identified.

Keywords

Regional innovation system loosely coupled systems small-world network relationship strength knowledge flow

A regional innovation system is a complex network system in which subjects use resources to collaborate in order to achieve innovation under the influence of policy systems and complex relationships in a specific economic region. The effective operation of such a system can help enterprises in a region realise technological innovation, accelerate scientific and technological achievements, and enhance the competitiveness of the regional economy. A regional innovation system serves as the basis for a country to realise technological innovation and ensure international competitiveness (Audrestch et al., 2016; Fu & Jiang, 2019). At the National People’s Congress and Chinese People’s Political Consultative Conference held in March 2021, Chinese Premier Li Keqiang clearly pointed out from a government work report that China will improve its national innovation system in the next five years through innovation-driven development and by accelerating the development of a modern industrial system. The country plans to adhere to the core position of innovation in the overall context of China’s modernisation and to adopt scientific and technological self-reliance as a strategic approach to national development.

In improving its innovation system, China has adopted a development model of regional coordination. The establishment of the integration of Beijing-Tianjin-Hebei and the planning of the Guangdong-Hong Kong-Macao Greater Bay Area have adopted a regional coordinated development model. In the context of economic globalisation, the complexity and uncertainty of regional innovation development have become more obvious, the limitations of a single innovation subject have intensified, and the promotion of cooperation and coordination in the development of regional innovation systems has become prominent. In this context, cooperative relationships within the regional innovation system and how multiple agents form collaborative innovation have become the focus of scholars. Recent research on regional innovation mainly focuses on system dynamics, performance evaluation, and sustainable development. There are few studies on the relationship between subjects in the regional innovation system, especially on the impact of relationship strength on knowledge flow. This work starts by focusing on the strength of the relationships between subjects of the regional innovation system, combined with the loosely coupled system, and observes the characteristics of knowledge flow within the regional innovation system under relationships of varying strength. This will provide theoretical support for the construction of China’s regional innovation system and for the improvement of the country’s national innovation system.

Literature Review

As regional innovation systems are a source of regional economic development, these systems have been widely studied by scholars at home and abroad, and research in this field has shifted from reductionism to systems theory. Most scholars regard a regional innovation system as a non-linear, open, complex system with a certain area, city and country as the boundaries. One of the main research directions is to examine the driving force of regional innovation systems. Italian scholars have studied how global connectivity can promote the development of a country’s regional innovation system (Berman et al., 2020). Scholars have also elaborated on the role of social capital as link in a regional innovation system and analysed the contribution of social capital to regional innovation development in the particular case of the Basque region (Amonarriz et al., 2019). Some scholars have analysed the impact of a company’s geographic location on its innovation results, especially its impact on the complexity of results (Tavassoli & Karlsson, 2021). Research results on the internal driving force of regional innovation systems are also rich, and the research methods adopted are diverse, including economic and chemical models such as the production function (Ott & Ronde, 2019), the threshold regression mode (Su & An, 2018) and chemical oscillation reaction (Su & Liu, 2019). These methods cleverly cope with the complexity of regional innovation systems. Another research issue that scholars focus on is the measurement of regional innovation systems. This stream of research is mostly based on statistical data and uses a variety of measurement methods to address research question and draw conclusions. For example, scholars have combined cluster analysis with Bayesian discrimination to determine the advantages and disadvantages of regional innovation systems in typical Chinese cities (Liang et al., 2019). The entropy weight and fuzzy set methods have been used to calculate innovation quality in different regions of China (Zhang & Li, 2020). Scholars have used two-stage data envelopment analysis to evaluate the efficiency of technology development and commercialisation in Korea (Min et al., 2020). Scholars have also used logistics equations, theory of acoustic waves, network models and other models to study the coordination abilities of regional innovation systems, knowledge transfer in the regional innovation system, and the characteristics and development trends of interregional innovation association networks (Arranz et al., 2019; Chen et al., 2020; Pan et al., 2020; Su & Li, 2020). In addition to the above two traditional research directions, the sustainable development of regional innovation systems has also become a topic that scholars have paid more attention to in recent years. Rapid economic development leads to many problems, such as energy security and environmental pollution. Spatial econometric model analysis, social network analysis and other methods are used to promote the sustainable development of regional innovation systems. It has been proposed that the establishment of a regional environmental joint governance system can form the theoretical basis for improving regional environments and promoting innovation and sustainable development (Su & Yu, 2020; Morales & Sariego-Kluge, 2021). Environmental governance requires the realisation of green and low-carbon innovation from the source, and the search for a green innovation path should start by transforming the industrial structure, optimising the support structure, and strengthening government behaviour (Trippl et al., 2020). The establishment of low-carbon city pilot programs and the adoption of new carbon emission accounting methods can significantly improve regional industrial structures and promote regional sustainable development (Peng et al., 2021; Zheng et al., 2021).

The above research on regional innovation systems has three main focuses: system dynamics, performance evaluation and sustainable development. These three streams of research regard a regional innovation system as a complex whole, and the goal is to achieve the optimal solution of the system. However, most scholars ignore the relationship between subjects in this complex system and do not consider the network structure formed by subjects. Small-world networks are ubiquitous in various fields. Due to the short feature paths of small-world networks and the large aggregation coefficients, a small-world network structure can promote the overall goal of a system. Scholars have found that the small-world network structure can promote innovation in nanotechnology (Shi & Guan, 2016), optimise the allocation of resources to promote product innovation (Ozkan-Canbolat & Beraha, 2016) and enhance the efficiency of innovation diffusion (Zhang et al., 2016). Empirical evidence shows that if the exchanges between inventors and other inventors in a company form a small-world network, this can greatly enhance the innovation ability of inventors and company cohesion (Lengyel & Eriksson, 2017). Most of the research on relationships and innovation discusses the relationships between people in an enterprise, such as the relationships between leaders and employees and the innovation atmosphere among employees (Christiansen et al., 2014; Ge & Sun, 2020). Existing research does not correlate relationship strength with the network structure of a regional innovation system, and it fails to explain how the elements of a regional innovation system change when the strength of intersubject relationships changes in the system and thus affects the entire system.

The contributions of this article to the literature are as follows. First, based on real statistical data, a regional innovation system with the characteristics of a small-world network is constructed based on the proportion of universities, enterprises, and research institutes in the real world. Thus, the subjectively drawn influence of the number of subjects on the simulation results is eliminated. Second, the study applies loosely coupled theory to research the relationship strength in regional innovation systems. Corresponding to the network-modularity (N-M) matrix of loosely coupled theory and regional innovation systems with different relationship strengths; the characteristics of knowledge flow in a system under different relationship strengths are observed. Third, based on the characteristics of knowledge flow, this study analyses the influence of the relationship strength of subjects on knowledge flow to provide a new analytical perspective and guide policy to help China develop a highly efficient regional innovation system.

Research Design

Small-World Network

The origin of the small-world phenomenon is the ‘six degrees of separation theory’ proposed by psychologist Milgram. Milgram believed that in social networks, a person is connected to any stranger in the world by no more than five intermediaries (Kleinberg, 2004). Inspired by Milgram, in 1998, Watts and Strogatz (1998) conducted in-depth research on human social networks and proposed the famous W-S small-world network model. The small-world network model is between a regular network and a random network. It can be generated by a regular network with a certain probability p, broken key and reconnection, as shown in Figure 1.

Figure 1.

Source: The authors.

We usually consider network structure in terms of clustering coefficients and characteristic path lengths. The agglomeration coefficient is also called the clustering coefficient and describes the degree of connection between adjacent nodes in a network. The characteristic path length represents the average value of the shortest distance connecting any two nodes in a network. Considering a small-world network with the above two indicators, the network has the characteristics of a high agglomeration coefficient and a short characteristic path length.

The small-world network model has been widely applied in scientific research, such as in internet science research, infectious disease model research, social journalism research and other fields (Liljeros et al., 2001; Albert & Barabasi, 2002; Ruan & Li, 2016). A regional innovation system can also be regarded as a complex system with the characteristics of a small-world network. In a regional innovation system, the mutual communication between the main bodies is not fixed. Subjects decrease or increase their exchange frequency according to a certain rule, similar to the process found in a regular network, by breaking the key and reconnecting to form a small-world network (Opashl et al., 2017). Under the original structure, the main bodies reduce communication frequency until no relationship is broken, and they increase communication frequency to form a new connection is reconnection. In this way, a short social distance is established between the main bodies. In addition, a regional innovation system is a complex system (Guan, 2016) composed of several subsystems. If the subsystems can exist stably, the aggregation coefficient of the network must be large. A regional innovation system is a small-world network with high agglomeration coefficients and short feature paths. Therefore, this article constructs a simulated regional innovation system with the characteristics of a small-world network for simulation research.

Loosely Coupled Theory and Relationship Strength in a Regional Innovation System

The ‘loosely coupled’ concept originated in biology (Orton & Weick, 1990). In the 1970s, American scholar Weick took the lead in applying this idea to organisational analysis and proposed loosely coupled theory. Then, Orton and Weick summarised loose coupling theory and proposed tight coupling and non-coupling from the perspective of integrity and independence. They believed that when the integrity of a system masks the independence of each module, the system is tightly coupled, and when the independence of the module is more prominent and each part of the module fails to reflect the integrity, the system is uncoupled. A loosely coupled system is between tightly coupled and uncoupled systems. In a loosely coupled system, there is a response mechanism between each module. Modules maintain a certain relationship and show certain integrity. However, this integrity does not obscure the independence of each module. Orton and Weick believed that the reason for the formation of loosely coupled systems is that, in such systems, the connection between modules is accidental and indirect. With such connection, there is no rule that continues to affect each module (Shen et al., 2017).

In a regional innovation system, the strength of relationships plays a vital role in the innovation process. Some scholars have analysed the relationship strength of subjects in regional innovation systems from the perspective of contact time, investment of resources, scope of cooperation and reciprocity. However, research neglects that each subject and each module in a regional innovation system are independent. It is difficult to describe the relationship strength between different subjects completely with a single, certain rule. The dominant logic of each subject and module is different. The determination relationship of the same rule cannot accurately describe the relationship strength of a regional innovation system. Loosely coupled theory provides us with new ways to describe the strength of relationships within regional innovation systems (Papadonikolaki, 2018).

The rationality and uncertainty of a regional innovation system, the contradiction between the independent behaviours of each module and the consistency of the goal can be explained by loosely coupled theory. The independent logic of each subject in a regional innovation system can be understood as the simple task of the independent operation of each module in this complex system. The common goal of ultimately achieving innovation is the embodiment of the system as a whole and the complex task of the entire system. According to the theoretical basis of Orton and Weick (1990) and the research of other scholars in recent years, we can establish a relationship between the loosely coupled theoretical image N-M matrix (shown in Table 1) and the strength of the relationships between subjects in regional innovation systems.

Table 1.

Loosely Coupled Theory Diagram: N-M Matrix.

	Low Module Independence	High Module Independence
High network integrity	Tightly coupled system	Loosely coupled system
Low network integrity	Non-system	Discrete uncoupled system

Source: The authors.

Relying on the research entry point of Orton and Weick (1990), we also use the perspective of independence and holism to discuss the relationship between loosely coupled theory and the relationship strength of subjects in a regional innovation system. When the relationships between subjects in a regional innovation system are extremely weak, the links between the subjects and modules can hardly be established and the interaction between subjects is almost non-existent. This is a network with low integrity. At the same time, due to the lack of exchange of elements with the outside world, it is difficult for each subject and module to complete the tasks of independent units. Therefore, when the strength of the relationships is extremely weak, the regional innovation system has low network integrity and low module independence, corresponding to the non-systematic and non-organised system in the N-M matrix of the loosely coupled theory diagram. When the strength of relationships between subjects increases slightly, each subject and module can exchange knowledge, funds, manpower and other elements with the outside world, which can help subjects complete their independent tasks. However, due to the weak relationships between subjects, the friction coefficient of the element exchange is too large, the system integrity is still low and the system is a discrete uncoupled system. If the strength of the relationships between subjects in the regional innovation system is high, the exchange and flow of elements will frequently occur between subjects and modules. In this process, each subject and module will ensure that its own tasks can be successfully completed. This structure also presents coupling characteristics under a strong relationship, that is, subjects have independent goals, independent identities, and independent functions, and the loosely coupled state of integration is achieved as a whole. However, when the relationship strength is increased, this loosely coupled state will be broken. The strong relationship strength breaks the independence of each unit and each subject; thus, under this relationship strength, the independence of the subjects in the system will be weakened and the entire system will show a high degree of integrity. The independent functions, goals and identities of each subject will be covered by the overall task, forming a tightly coupled system. In this system state, the environment outside the system will quickly have a huge impact on every subject in the system, resulting in a decline in system stability.

Based on the above analysis, we found that under relationships of varying strength, subjects of the regional innovation system and the entire innovation network show different characteristics. Taking network integrity and module independence as a starting point, we found that the regional innovation system under relationships of differing strength has similar structural characteristics to those of the four systems explored by loose coupling theory. Based on this, the relationship between the strength of relationships and the four systems is established. As shown in Table 2.

Table 2.

A Diagram of Loosely Coupled Theory: N-M Matrix of the Relationship Strength Between Subjects in a Regional Innovation System

Relationship Strength	Corresponding System Type	Characteristic
Extremely weak	Non-system	Low module independence and low network integrity
Weak	Discrete uncoupled system	High module independence and low network integrity
Strong	Loosely coupled system	High module independence and high network integrity
Extremely strong	Tightly coupled system	Low module independence and high network integrity

Source: The authors.

Knowledge Flow in Regional Innovation Systems

As the most important resource of a regional innovation system, knowledge is the foundation of regional innovation. The innovation process of a regional innovation system depends on the knowledge base held by subjects (Asheim & Coenen, 2005, 2006; Sung & Choi, 2018). The existing knowledge base of a subject in a regional innovation system is combined with new external knowledge to form a new knowledge system. Through the continuous overlapping and replacement of knowledge, a subject’s knowledge innovation is promoted to achieve technological innovation (Lai et al., 2016). In this process, three subjects in the regional innovation system play a vital role. The first are universities, which play a role in the creation of native knowledge in regional innovation systems. Colleges and universities generate native knowledge through technological innovation, research and development (R&D) and expansion, and create a source of knowledge. Second, research institutes, with a role similar to that of universities, are indispensable for the creation of original knowledge. From a functional point of view, universities are more inclined to generate original knowledge from scratch, while research institutes engage more in knowledge-based incubation. From the perspective of knowledge flow, colleges and scientific research institutes create and generate native knowledge; use college science and technology parks, incubators, scientific research offices and other institutions to transform knowledge into results; and connect with the third important subject, that is, enterprises. Research traditionally believes that enterprises are the party that accepts knowledge. However, with the gradual development of China’s economy, many enterprises also engage in their own technology R&D activities and rely on actual market activities to generate a large amount of native knowledge, forming a knowledge flow feedback mechanism (Huang & Chen, 2020; Li et al., 2017; Zhou, 2014).

Knowledge flow is the process of copying knowledge from one subject to another, but knowledge loss occurs during the copying process. The types of knowledge flow are mainly transactional and broadcast flows. In transactional flows, the conditions may be completely different in different environments, so in the research process, broadcast flow is more suitable for the flow analysis of a fixed network structure (Cowan et al., 2006). Cowan et al. (2006) proposed to judge the effect of knowledge flow from two aspects: the efficiency of knowledge flow and the balance of knowledge distribution. They believed that the efficiency of knowledge flow can be determined from two aspects: one is the mean of knowledge and the other is the flow speed of knowledge. The mean of knowledge reflects the average knowledge level of each subject in a group or system. The speed of knowledge flow reflects the speed of knowledge diffusion. The less time taken to reach a certain knowledge mean, the better the effect of knowledge flow within the group or system. Knowledge variance is an important indicator in considering the balance of knowledge distribution. When a system or group shows low knowledge variance, the balance of knowledge distribution is better. Many scholars also believe that when knowledge flow in a system presents a high mean, low variance and a high flow rate, it will show the emergence characteristics of its system (Wang & Zhang, 2009, 2011, 2013).

The number of patent applications of an enterprise reflects its technical capabilities and creativity and represents the innovation ability and knowledge level of the enterprise to a certain extent (Chen et al., 2018; Chiu & Lin, 2019; Xia et al., 2020). The number of patent applications from universities and scientific research institutions is considered a concentrated expression of knowledge creation capabilities. Thus, this article uses the number of patent applications to represent the knowledge level of each subject.

Data Sources and Modelling Rules

In previous studies, scholars have established small-world networks with a self-defined number of subjects to conduct simulation research on regional innovation systems. For example, scholars establish a small-world network with 100 subjects and give each subject a different role according to their subjective wishes, such as universities, enterprises, research institutes and financial institutions. This modelling method ignores real-world small-world networks and the true proportion of heterogeneous subjects. The functions and roles of different subjects in the regional innovation system are different. If the number of subjects is set subjectively when setting the simulation parameters, the structure and function of the regional innovation system generated by simulation will differ from those of the actual regional innovation system, which will affect the characteristics of knowledge flow. Therefore, this article builds on data from 2019 included in the Statistical Yearbook of the National Bureau of Statistics and builds a small-world network of regional innovation systems based on the actual number of heterogeneous subjects and the level of knowledge to eliminate the influence of subjective assignment on the flow of knowledge. Based on these data, a simulation study is conducted to explore the regional characteristics of knowledge flow when the strength of the relationships between subjects in the innovation system changes.

This study uses Netlogo 6.1.0 software to build a small-world network of regional innovation systems with true proportions. The specific code and data are shown in Table 3.

The basic knowledge level of universities, enterprises, and scientific research institutions are all coded as knowledge, and the value is the number of patent applications of three different subjects in 2019. The code and value only represent the basic value of the small-world network of the regional innovation system constructed in the simulation research. The number of patent applications represents the level of knowledge of this type of subject. We convert the actual data of the number of patents into the level of knowledge in the simulation system. The flow is an element of the system knowledge. This does not mean that patents for applied by different subjects can flow between subjects.

According to the data in Table 3, we build a small-world simulation model of a regional innovation system. The main data, structure, and construction principles are as follows.

Table 3.

Basic Data Scale of the Small-World Simulation Model of a Regional Innovation System

Name	Code	Value
Number of universities	University	2,663
Number of industrial enterprises above a designated size with R&D activities	Enterprise	104,820
Number of scientific research and development institutions	Research centre	3,306
Number of patent applications accepted by colleges and universities	Knowledge	320,790
Number of patent applications from industrial enterprises above a designated size	Knowledge	957,298
Number of patent applications accepted by scientific research and development institutions	Knowledge	61,404
Relationship strength	strength	0–1

Source: China Statistical Yearbook 2019, http://www.stats.gov.cn/tjsj/ndsj/2019/indexch.htm

Number of Subjects

To better observe the characteristics of knowledge flow, the small-world simulation model compresses the sum of the three types of heterogeneous subjects—universities, enterprises and scientific research institutions—to 500, which includes 12 universities, 473 enterprises and 15 research institutes.

Knowledge Level

The level of knowledge is reduced in proportion to the number of subjects. Therefore, the sum of the basic knowledge levels of twelve universities is 1,445, and the sums of the basic knowledge levels of enterprises and scientific research institutions are 4,312 and 277.

Knowledge Distribution

To make each subject’s knowledge level not zero and reflect the differences among homogeneous subjects, this study randomly assigns an initial knowledge value to each university and scientific research institute through the command ‘random-normal’. The sum of knowledge of the twelve universities is 1,445, and the distribution of knowledge levels of each subject tends to be normal. The sum of the knowledge of the fifteen scientific research institutions is 277, and the distribution of the knowledge level of each subject is close to normal. There are 473 enterprises in this model. Domestic scholars believe that in studying of the knowledge distribution of enterprise clusters, China’s enterprise clusters can be divided into two types: market-based and central-satellite clusters (Liu et al., 2014; Zhang et al., 2018). In the simulation system, the enterprises are industrial enterprises that are above a designated size and engage in R&D activities, and their cluster characteristics should conform to the central-satellite enterprise cluster. The knowledge distribution is similar to the Poisson distribution. Therefore, in the simulation program, the ‘random-Poisson’ command assigns the initial knowledge of the enterprise. The sum of the knowledge of 473 enterprises is 4,312, and the distribution of the knowledge level of each subject approaches the Poisson distribution.

Small-World Network Construction

First, a regional innovation network with a network density of 8% is formed. Subjects randomly cut off existing connections with probability p = .09 and re-establish connections with other subjects. In their research, Cowan et al. (2006) found that a small-world network constructed with a small probability of p = .09 has the highest knowledge flow efficiency. Therefore, this study uses this probability to construct a small-world network of regional innovation systems.

Relationship Strength

We set the relationship strength slider with a value range of 0–1, and we choose different strength values to represent four different relationship strengths corresponding to four types of systems according to loosely coupled theory.

Knowledge Flow

In alignment with previous studies, we assume that subject m has a knowledge value of K_mt₀ at time t₀, that subject m has a relationship to subject n and that the relationship strength is r. The knowledge value of n at time t₀ is K_nt₀. If the flow condition is satisfied K_mt₀ – K_nt₀ > K_nt₀ × (1-r)/10, then knowledge flow occurs, and at time t₁ after the flow occurs, the knowledge of subject n is K_nt₁ = K_nt₀ + K_nt₀ × r/10. (Wang & Zhang, 2009). In the simulation model, each agent will choose the agent that has a connection with it and is the closest to the subject to undergo knowledge flow according to the above conditions. The distance here refers to the distance in the Netlogo world. This does not mean that in a real regional innovation system, a subject will use geographical distance as the criterion to generate knowledge flow. Distance here represents the preference for the subject’s knowledge flow in the system (Wang & Zhang, 2010).

Simulation Results and Analysis

According to the construction principle of the simulation model and the mode of knowledge flow, the characteristics of knowledge flow are observed by changing the relationship strength slider.

Figure 2 shows the characteristics of knowledge flow when the relationship strength is 0.2. In this case, the increasing trend of the mean value of knowledge is not obvious, indicating that the growth rate of knowledge is slow and the variance of knowledge is slowly decreasing. The change trend of the two is similar to a linear change. After 100 steps of simulation, the system knowledge average is 31.09 and the knowledge variance is 301.85, showing a low knowledge mean, high knowledge variance and a low knowledge flow rate.

Figure 2.

Source: The authors (simulation by Netlogo).

Figure 3 shows the characteristics of knowledge flow when the relationship strength is 0.4. Under the strength of this relationship, the system presents a discrete uncoupled system state. The slope of the knowledge mean curve rises slightly, changing from a quasi-linear change to a curve change, indicating that the knowledge flow rate is accelerating. The rate of decline of knowledge variance is also relatively fast, and a slight inflection point appears in the process of the decline of knowledge variance. After 100 steps of simulation, the mean value of knowledge is 72.94 and the variance of knowledge is 181.90. Both the mean value of knowledge and the flow rate of knowledge are improved relative to the non-system state and the variance of knowledge is further reduced, indicating that knowledge flow has reached a higher level in this state.

Figure 3.

Source: The authors (simulation by Netlogo).

Figure 4 shows the characteristics of knowledge flow when the relationship strength is 0.6. At this time, the small-world simulation model of the regional innovation system is a loosely coupled system. The knowledge mean is increasing rapidly, the slope of the knowledge mean curve is increased and the knowledge flow rate is accelerated. The knowledge variance curve shows two inflection points: the first inflection point accelerates the reduction of knowledge variance and the second inflection point makes the knowledge variance curve show an y-axis parallel trend. After 100 steps of simulation, the system knowledge average is 130.83 and the knowledge variance is 37.47. At this time, the flow of knowledge in the system is fast, the mean is high, and the variance is small, showing the emergence of knowledge.

Figure 4.

Source: The authors (simulation by Netlogo).

Table 4.

Characteristics of Knowledge Flow Under Relationships of Varying Strength

Relationship Strength	Knowledge Mean	Knowledge Variance	Knowledge Flow Rate	Corresponding System
Strength = 0.2	31.09	301.85	Slow	Non-system
Strength = 0.4	72.94	181.9	Slower	Discrete uncoupled system
Strength = 0.6	130.83	37.47	Rapid	Loosely coupled system
Strength = 0.8	470.37	1039.69	Extremely rapid	Tightly coupled system

Source: The authors (simulation by Netlogo).

Figure 5 shows the characteristics of knowledge flow when the relationship strength is 0.8. In this tightly coupled state, the knowledge flow rate and the mean value of knowledge show an explosive trend. However, at the same time, the increase in knowledge variance shows that the imbalance of the system’s knowledge distribution will further increase in this state. During the flow of knowledge, the slope of the mean curve of knowledge continues to increase, indicating that the flow of knowledge continues to accelerate. At the same time, the oscillating rise of the knowledge variance curve shows that during the flow of knowledge, subjects are constantly breaking the balance and reaching a new status. However, the imbalance of knowledge distribution has not been improved. After 100 steps of simulation, the system knowledge average is 470.37 and the knowledge variance is 1039.69.

Figure 5.

Source: The authors (simulation by Netlogo).

The simulation depicts the knowledge flow between subjects in the regional innovation system under different strengths, and the data in Table 4 are obtained.

The simulation model presents the characteristics of knowledge flow in the system under different relationship strengths. The simulation results show that under different relationship strengths, the system’s integrity and independence are quite different, forming non-systems, discrete uncoupled systems, loosely coupled systems and tightly coupled systems. In different systems, the flow of knowledge shows different characteristics. When the relationship strength is 0.6, the system shows the characteristics of a loosely coupled system. The flow of knowledge in the system shows the emergence of a high knowledge flow rate, a high knowledge mean and low knowledge variance.

When the strength of the relationship is extremely weak, the simulation world shown in Figure 6 is obtained, and there is no effective knowledge flow between subjects. In this world, most of the knowledge is concentrated in universities, knowledge has not been transmitted to enterprises through connections and scientific research institutions have not played an intermediary role. The resistance coefficient of knowledge flow between subjects is too large to meet the conditions of knowledge flow, so subjects in the system cannot establish effective connections and cannot effectively spread knowledge. In this case, only subjects with huge knowledge gaps and interconnected subjects can form a knowledge flow, and in the flow process, knowledge loss is serious, showing a non-systemic and non-organised situation. Only a very small number of peer-to-peer subjects form knowledge flows. This finding corresponds to the actual world, where enterprises with low knowledge levels cannot effectively communicate with core enterprises, universities and scientific research institutions due to their inability to communicate effectively. They can improve their knowledge level only through simple imitation and copying. However, due to the lack of communication and communication, imitation and replication cannot achieve a real leap in knowledge, so it shows the characteristics of slow flow of knowledge. In the original state of the system, the knowledge distribution is unbalanced. Imitation and replication cannot quickly increase the knowledge level of low-knowledge subjects, and it is difficult to eliminate the imbalance of knowledge distribution in the system. Therefore, knowledge variance cannot be effectively reduced.

Figure 6.

Source: The authors (simulation by Netlogo).

The resistance of information transfer between subjects is lower when the relationship strength is weak than when the relationship strength is extremely weak, which provides a relatively convenient condition for knowledge flow. The simulation world is shown in Figure 7. The university’s knowledge level still leads the region, and it can spread some knowledge to enterprises. The intermediary role of scientific research institutions has also begun to manifest. At this time, the characteristics of independence in a small area of the region are presented, but the system’s integrity has not been developed. Enterprises with high-knowledge subjects such as universities and scientific research institutions improve their knowledge levels faster due to the reduction of resistance to knowledge flow and larger knowledge gaps, resulting in an effective flow of knowledge in a small area. However, enterprises on the edge will still be unable to establish effective contact with other subjects due to the existence of resistance and will form ‘islands’ that prevent them from effectively improving their knowledge level. From a regional perspective, under the strength of this relationship, some regions with core knowledge subjects have realised the effective flow of knowledge and the average value of knowledge can be rapidly improved. However, the existence of ‘islands’ in the system makes the system’s integrity weak, and there is still an unbalanced knowledge distribution. In addition, under the current relationship strength, enterprises cannot cooperate with universities and scientific research institutions to establish an effective feedback mechanism. They will encounter bottlenecks in their continuous development, and the flow of knowledge will slow down. After the average knowledge reaches a certain level, it cannot continue to grow.

Figure 7.

Source: The authors (simulation by Netlogo).

In the case of strong relationship strength, the resistance of knowledge flow between subjects is further reduced, the speed of knowledge flow is accelerated and the system exhibits high module independence and high network integrity. The simulation world is shown in Figure 8. At this time, enterprises, universities and scientific research institutions can establish effective connections. In an area centred on a university, a scientific research institution or a core enterprise with a high level of knowledge, all enterprises can realise the diffusion and dissemination of knowledge, forming a higher average value of knowledge, and there are no longer ‘islands’ in the entire system. More importantly, a feedback mechanism can be established between the enterprise and the university, which promotes the improvement of the knowledge level of the university, breaks the bottleneck of the discrete uncoupled system and enables the average value of knowledge to continue to rise. At the same time, due to the absence of ‘islands’ in the system, low-knowledge enterprises can also effectively improve the level of knowledge through the flow of knowledge so that the entire system presents the emergence of a high knowledge flow rate, a high knowledge mean and low knowledge variance.

Figure 8.

Source: The authors (simulation by Netlogo).

In the case of extremely strong relationship strength, there is almost no resistance to the flow of knowledge between subjects and knowledge diffusion is rapid. The simulation world is shown in Figure 9. There are irregularly distributed subjects with high knowledge levels, including universities, enterprises and scientific research institutions. At this time, the system’s network integrity is significant, but the regional independence is masked. During the rapid diffusion of knowledge, the core subject cannot be found in an area. The average value of knowledge in the whole system is rapidly improving, but the balance of knowledge distribution is poor. In the initial stage of knowledge diffusion, enterprises with low knowledge levels will be more likely to acquire new knowledge. In the process of improving its knowledge level, the knowledge variance of the system is reduced. However, due to the small resistance to knowledge flow, knowledge flow can also occur between two subjects with a small knowledge gap, which will not continue to inject knowledge into enterprises with low knowledge levels, resulting in an inflection point in the knowledge variance curve and an unbalanced knowledge distribution further improve.

Figure 9.

Source: The authors (simulation by Netlogo).

Main Research Conclusions and Prospects

A small-world simulation model of a regional innovation system is constructed. From the perspective of module independence and network integrity, the relationship strength of subjects in regional innovation systems and loosely coupled theory are combined. The four states of system relationship strength—extremely weak, weak, strong and extremely strong—correspond to the four types of systems in the loosely coupled theoretical image N-M matrix, that is, non-systems, discrete uncoupled systems, loosely coupled systems and tightly coupled systems. The simulation revealed the knowledge flow characteristics of subjects among regional innovation systems under four different relationship strengths and reached the following conclusions:

The change in the relationship strength of a regional innovation system will make the system’s integrity and independence show different states. When the relationship strength is extremely weak, the system presents low independence and low integrity; when the relationship strength is weak, the system presents high independence and low integrity; when the relationship strength is strong, the system presents high independence and high integrity; and when the system strength is extremely strong, the system exhibits low independence and high integrity.

Changes in the relationship strength of regional innovation systems have an impact on knowledge flow.

When the relationship strength is extremely weak, the knowledge flow rate in the system is extremely slow, the knowledge mean is low, the knowledge variance is large and the knowledge flow efficiency in the system is low, which cannot guarantee the stable operation of the regional innovation system.

When the strength of the relationship is weak, the flow of knowledge in the system is slow, the mean of knowledge is low and the variance of knowledge is large. Knowledge in the system can flow effectively in a certain area, but it will form an ‘island’ in the system, which is not conducive to the long-term development of systems.

When the relationship strength is strong, the knowledge flow rate in the system is faster, the knowledge average reaches a higher level and the knowledge distribution is balanced and reasonable, showing the emergence of a high knowledge average, a high knowledge flow rate, and low knowledge variance. At this time, the regional innovation system is in the best state. Effective communication can be established between subjects, and knowledge can flow effectively within the system.

When the relationship strength is extremely strong, the knowledge flow rate in the system is the fastest and the knowledge mean is the highest, but the knowledge variance also declines first and then rapidly increases with the flow of knowledge. The knowledge distribution is more uneven than in the initial state. The lack of continuous input of knowledge to subjects with low levels of knowledge leads to increased polarisation. Under this state, the regional innovation system continues to be in an unbalanced state.

Based on the above analysis, this study believes that research on the impact of the relationship strength between regional innovation departments on regional innovation can also be carried out from the following aspects:

In this study, since the indicator of relationship strength is difficult to quantify, no specific value has been calculated through empirical research. Instead, it assumes different values to correspond to different systems in loosely coupled theory. In future research, we will quantify these indicators by way of empirical research. The data can be used to further verify the influence of relationship strength on regional innovation.

Refine the knowledge categories in the system. In this study, the number of patent applications is converted into the initial knowledge value of each subject, and there is only one kind of knowledge that can flow between different subjects. However, when different subjects establish a knowledge flow relationship, their knowledge and categories should be different. In future research, the categories of knowledge can be distinguished to better explore the flow characteristics of different types of knowledge when relationship strength changes.

Footnotes

Data Availability

The data used to support the findings of this study are included in the study.

Declaration of Conflicting of Interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This study was supported by National Natural Science Foundation of China (71774036, 72074059), Social Science Foundation of Heilongjiang (20GLB120), and Natural Science Foundation of Heilongjiang Province (QC2018088).

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