Synergy and Correlation Optimization Analysis of Innovation System and Institutional Governance System from the Perspective of Cluster Ecosystem

Innovation and institutional governance are the key enabling factors of cluster ecosystem development. Its synergistic effects play an important role in enhancing ecosystem competitiveness. In this paper, pseudocode language is applied to cluster ecosystem cooperative model reasoning. -e coordination and optimization of the innovation system and institutional governance system were studied in a biomedical cluster. Besides, Pearson algorithm was used to test the correlation degree of elements in three Chinese biomedical clusters. -e results show that, in Zhangjiang and Nanchang biomedical clusters, the synergistic correlation coefficient between the innovation system and the institutional governance system fluctuates around 0.8. However, in Tonghua biomedical cluster, the synergy correlation coefficient fluctuated around -0.2. -e fluctuation range between the two clusters was large. After adjusting the range of order parameters, the rank of synergy trend was Zhangjiang>Nanchang>Tonghua. Finally, further analysis shows that Zhangjiang and Nanchang biomedical clusters can achieve the optimal synergy state by adjusting innovation and institutional governance, but Tonghua cannot. -erefore, the collaboration between the innovation system and institutional governance system provides some reference for the high-quality development of the cluster ecosystem.


Introduction
Cluster gathering has become a typical form of rapid development in China under the influence of the socialist system with Chinese characteristics. e industrial cluster has become an important tool to enhance China's global competitiveness. e formation and growth of clusters have obvious ecological characteristics [1]. As a compound system, a cluster ecosystem is an effective way to improve regional economic competitiveness [2]. In China, many industries are currently overcapacity [3]. is problem directly affects the healthy development of the cluster. With the proposal of China's "dual carbon" goal, the ecological development of clusters has become the new direction. e improvement of innovation ability is an important link to promote the green development of clusters [4]. e emergence of intelligent manufacturing, big data, artificial intelligence, and other emerging technologies have brought scientific and technological revolution and industrial transformation under the new normal. It has spawned a large number of new technologies, new models, and new forms of business. is state provides opportunities for the development of clustered ecosystems. In 2020, the Torch Center of the Ministry of Science and Technology of China released the "Opinions on Deepening the High-quality Development of Innovative Industrial Clusters." e ministry pointed out that the high-quality development of clusters focuses on the major strategic needs of the country and builds a modern regional economic system. Innovation can promote the evolution of the cluster ecosystem to a higher level and strengthen the correlation of scientific activities within the system. Innovative industrial cluster is a typical form of cluster ecosystem and plays an important radioactive effect on regional economic development. It can stimulate the innovation vitality and power of enterprises in the cluster and promote the conquest of key core technologies. Many related industries are radiated and trigger the development. is can realize the cluster from the low order chaos to the evolution of the higher-order order [5]. erefore, the dynamic evolution of the cluster ecosystem is a transition process from a small cluster to a large cluster and from low quality to high quality. It is well known that the cluster ecosystem has the characteristics of mutualism, resource sharing, self-organization evolution, and cooperation in opening [6]. is enables the cluster ecosystem to form a geographical range of multiple industries to cooperate, a large number of organizations and members into a community of common destiny. Many industrial clusters are not born naturally but under the arrangement of the government system in China [7]. is makes institutional governance have a great influence on the evolution of the cluster ecosystem. us, the improvement of the quality and efficiency of the cluster ecosystem cannot be achieved by a single factor. How to solve the high-quality development of a cluster ecosystem has become an urgent problem.
In conclusion, the main innovations of this paper are as follows: (1) this paper uses the combination of origin method and pseudocode to sort out the synergy model of cluster ecosystem. (2) is study focuses on the collaborative development of innovation and institutional governance in the cluster ecosystem. Rather than an accumulation of subsystems, it is an in-depth excavation of the correlation degree of elements in each system through the sequence parameter variables. It aims to achieve high-quality development of the cluster ecosystem in the process of dynamic competition and cooperation.

Cluster Ecosystem and Institutional Governance.
Cluster ecosystem grants cluster a world-class competitiveness [8]. China's cluster development occurs more from policy incentives, financial support, and other institutional means of governance [9]. Several researchers have proved that system governance can improve cluster innovation performance [10]. erefore, institutional governance has become the daily management activities of cluster ecosystem [11]. Innovation institutional governance was first proposed by Douglas North [12]. Institutional governance mainly involves control activities from the perspective of institutional innovation behavior to further stimulate and encourage the innovation atmosphere. Governance measures, regulations, procedures, and other institutional behaviors are adopted to regulate the innovation activities of the cluster ecosystem. Hence, they provide a standardized, scientific, and procedural development environment for a high level of cluster development [13]. Some scholars believe that the institutional governance of the cluster ecosystem has become the basis for supporting the sustainable development of organizational activities [14]. e governance of relationships within the cluster ecosystem can improve resilience and resist external risks [15]. Liu believes that the governance of the cluster ecosystem is closely related to the internationalization ability, which provides a direction for the exploration of national competitiveness [16]. From the perspective of ecological symbiosis, Yu and Sui discussed the realization of urban cluster ecological system under the management of symbiosis mechanism. It ensured the exchange of technology, knowledge, information, and other resources [17]. Some regions have regarded the cluster ecosystem as a model of industrial transformation and development [18].
Some scholars believe that the cluster ecosystem needs to take a professional governance. Nie et al. believe that the cluster ecosystem has endogenous power systems, such as capital, talents, technology, and other power resources support. Such systems are closely related to the professional governance of the cluster itself [19]. In terms of the institutional governance of the enterprise innovation cluster, Sun et al. carried out in-depth excavation [20] and divided the institutional governance into three layers of professional evolution structure namely. e layers include the genetic system governance [21], mediation system governance [22,23], and variant system governance [24]. In terms of national governance, Zhang et al. believe that the reform of the professional industrial system and policy improvement are important forces to accelerate the development of cluster ecosystem [25]. Over the past many years, many cluster leaders have made decisions in a "one-size-fits-all" perspective with often results lower than expected. In that regard, Coletti et al. believe that institutional governance should be closely designed to increase the flexibility of leader decision-making [26]. Maracha et al. pointed out that a new innovative industrial cluster ecosystem of advanced form, especially the digitization of governance, drives the collapse of cluster heterogeneous structures [27].

Cluster Ecosystem and Innovation.
e development of clusters requires the empowerment of innovative elements to promote their high-quality development [28]. e openness and sharing characteristics of the cluster ecosystem make the technical knowledge greatly transmitted internally and form a certain knowledge spillover effect [29]. However, such spillover is a "double-edged sword" for innovation. At present, many scholars have not conclusively established a clear relationship between knowledge spillover and innovation in clusters [30]. However, the dissemination of knowledge in clusters can certainly increase innovation benefits and improve the advancement of organizations in clusters [31]. e double-cycle development pattern provides huge market opportunities for clusters, attracts advanced elements from all over the world, produces the aggregation of innovative elements, and reduces transaction costs. Besides, it promotes the industry chain to get out of the low-end dilemma and promotes the formation of worldclass quality industrial cluster ecosystem [32]. e innovation and development of a cluster ecosystem are often accompanied by collaborative behavior in the process of cooperation [33]. Ying-Jing Chu et al. posit that such synergy can produce a spatial effect, which is conducive to the aggregation of innovation elements [34]. An organizational form with cross-industry and cross-region driving effects can be formed through the division of labor, cooperation, and collaborative innovation [35].
As a symbol of regional competitiveness, the cluster has several top innovation clusters that can promote regional development [36]. Germany was one of the first countries to attach importance to cluster development. Chen opines that Germany dares to break down barriers in close cooperation between industry, university, and research and build innovation clusters oriented at problem-solving and research [37]. Gao et al. pointed out that the close linkage between clusters and innovation not only promotes regional economic development but also forms cultural confidence. Such linkage is conducive to narrowing the regional development gap and promoting the generation of regional brands [38]. With the rise of "Internet +", cross-border e-commerce has become a key point of regional economic development. Fang Zhou found that the high-quality development of crossborder e-commerce clusters of foreign trade enterprises requires a systematic investment of innovative resources to form a collaborative ecological environment [39]. Similarly, Zhou et al. alluded that China is entering an era of highquality development. us, regional development cannot be separated from systematic innovation of clusters at the level of the value chain, industrial chain, and knowledge chain [40]. Wei et al. started from the perspective of innovation chain evolution in university science parks. ey explained the process of the evolution of regional innovation clusters into national innovation poles, which need systematic basic innovation support [41]. Wen et al. took the Guangdong-Hong Kong-Macao Greater Bay Area as an example to build world-class clusters. ey highlighted that the synergy between cluster driving and systematic innovation development is the key to achieving world-class competitiveness [42].
e system of governance and innovation for cluster has a great effect on the high quality of the ecological system. A few scholars agree on the perspective of the relationship between innovation and institutional governance study of the cluster. erefore, this article further explored the cluster innovation ecosystem under the innovation system and system management system of a collaborative relationship; the high-quality development of the cluster ecosystem provides a new direction.

Deduction of a Collaborative Model of Cluster Ecosystem
ere are many ways to deduce the cooperative model of a cluster ecosystem. is paper is enlightened by the research of Xie et al. [43]. e code backtracking algorithm is selected to deduce the cluster cooperation model. And the deduction process is described by pseudocode. So this is helpful to understand the realization logic of the collaborative model of innovation system and institutional governance system in cluster ecosystem. e specific deduction process is as shown in Algorithm 1.
Code TraceBack method was used to trace the formula file and function declaration to reflect the real needs [44]. It can be seen from formula file tracing (pseudocode lines 1-60) that cluster system T has the situation of synergy and accumulation state T. We set up the conditional program to obtain the coexistence. e preprocessing module parses its files to increase the matching degree of system T. So the cumulative effect formula of the system can be obtained (pseudocode lines [22][23][24][25][26][27][28][29][30][31][32][33][34][35]. e result output is pseudocode lines 32. Ergodicity exists in the traceability of the formula file and function declaration. e optimal static cooperation state is finally formed in pseudocode lines 37. is formal parameter is used in the line of code in the function body when the function is deformed. When tracing the function to the source, it will be unable to match with the code assembly instruction set, which requires instruction exit and redetermination. pseudocode lines 32 and 37 show that the cluster system can be regarded as several subsystems (pseudocode lines [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Further, the existence of synergistic effect is greater than nonsynergistic effect, and there is an optimal solution for such synergy.
is paper expanded the dynamic evolution, which is based on the traceability of static formula function. e order parameter functions are applied to static libraries to generate variable formula instructions with upper and lower bounds, while the dynamic system T r is judged. If the collaborative development within the cluster system reaches a certain state, function tracing is expected to become an instruction sequence rule. System T r can be made to reach a stable state in pseudocode lines 44 (pseudocode lines [41][42][43][44][45][46][47]. en, there is a certain range of order parameter λ ri . e more orderly and stable the system, the higher the weight in pseudocode lines 50 (pseudocode lines 48-53). At any time node t∊[t 0 , t 1 ], the order parameters of each subsystem are adjusted to store the function names with high matching correlation. is makes the dynamic composite system composed of formula file traceability and function traceability achieve stable coordination on the whole. By identifying each SourceFunc element, the program traces and compares the program source, which generate the corresponding dynamic composite system in pseudocode lines 55 (pseudocode lines 54-59). e degree of synergy presented is directly proportional to the degree of correlation between function values (pseudocode lines 48-60).

Variable Selection.
is paper draws on the existing research results. e R&D expenditure and number of R&D personnel are regarded as explanatory variables in innovation system [45,46]. According to the existing experience, 70% of the profits of innovative enterprises and high and new technology clusters come from technological innovation [47]. As a result, innovation income is another explanatory variable of innovation system [48]. e number of high-tech enterprises identified [20], Government S&T support funds [49], and system number [50] are taken as indicator variables in the innovation institutional governance system. In this way, the factors in the formula of the synergistic complex system can be constituted.

Mathematical Problems in Engineering
(1) Input: Source_code_path in Cluster ecosystem T.
(2) T: the relational function of the element (3) E g (T): compound relationship is formed in innovation cluster (4) T r : subsystem r in innovation System T (5) F n : a collection of synergies (6) F 0 : the optimal solution of innovate synergy (7) g: a system formed by collaboration (8) g 0 : form the optimal state of the new system (9) Opt: the optimal solution produced by E g (T) collaboration (10) λ r : set of order parameters in innovation system, λ r � (λ r1 , λ r2 , ...λ rn ) (11) λ ri: order parameter stability value (12) δ: the upper bound of the order parameter λ ri in System T steady state (13) η: the lower limit of the order parameter λ ri in System T steady state (14) μ r (λ ri ): order parameter degree of subsystem T r (15) μ r (λ ri ): order degree of complex innovation system (16) // ere are synergies between subsystems, which can form a cumulative effect. (34) Else no match mark into result of compare (35) End (36) If (∃F 0 ∊F n &&g � g 0 � F 0 f ) then (37) optE Print (opt E g (T) is synergy and static by T r ) (39) Else no match mark into result of compare (40) End (41) If (T r evolves stability&& λ ri ∈[δ ri , η ri ] � � true) (42) //In the process of subsystem evolution, there are order parameters with upper and lower limits, which make it develop stably. (43) en T r order variable μ r (λ ri ) (44) Print ( e result is μ r (λ ri ) � λ ri − δ ri /η ri − δ ri , 1 ≤ i ≤ l 1 , //It forms the degree of order of the stable evolution of the subsystem. (46) Else no match mark into result of compare (47) End (48) If μ r (λ ri ) ∈ [0, 1]&&weight (w i >�0&& j i�1 w i � 1) � � true then (49) //When the subsystem is stable and orderly, the weight is combined.
// is forms the stable and orderly degree of complex system evolution.
Else no match mark into result of compare (53) End (54)  Mathematical Problems in Engineering

Experimental Data Collection.
ree biomedicine clusters represent the level of development in north, central, and south China, which were used in this study. ey were Tonghua, Zhangjiang, and Nanchang biomedicine clusters. e data were selected from official channels such as China Torch Statistical Yearbook, Local Statistical Yearbook, and Government Statistical Bulletin. It was found that the 2012 yearbook is not the latest edition, and problems such as statistical data faults and inconsistent standards exist. erefore, in this study, the time range for data search is 2014-2020. Since the yearbook and other statistical data are based on the previous period, the data selected in this paper is from 2013 to 2019. Meanwhile, in terms of institutional governance, the official websites of local governments we searched are from directly managed departments. e provincial governments of the three biological clusters and the counted number of relevant systems were released each year. e specific data are shown in Tables 1-3.

Synergy and Correlation
Model. According to pseudocode lines 55, the synergy between the innovation system and institutional governance system in the cluster ecosystem means that each element in the two subsystems has a close correlation with the evolution of time.
e higher the correlation, the higher the degree of synergy between subsystems in the cluster. erefore, this study measured the correlation degree between systematic innovation and innovation institutional governance system to explore the collaborative quality further. Correlation degree was achieved through Pearson correlation and correlation ratio, providing ideas for promoting the development of high-tech innovation clusters. is paper refers to the results of Yu-Shao Chen et al. research [51], and the specific Pearson correlation model is shown in formula (1). Among them, the correlation coefficient is represented by c; the greater the absolute value of c, the stronger the correlation. e Pearson correlation coefficient model was constructed as follows: (1) c indicates the degree of correlation between the innovation system and the innovation institutional governance system. x i represents the set of all explanatory variables in the innovation system. e y i represents the set of all explanatory variables in the innovation institutional governance system. e magnitude of c is between [−1, 1]. If 1 ≥ c > 0, it shows a positive correlation. If −1 ≤ r < 0, this indicates that the two variables are negatively correlated. If c � 0, it means irrelevant.

Correlation Simulation.
In this study, pseudocode lines 32 was combined and correlation simulation carried out with empirical data. e data in Tables 1-3 were programmed with Matlab 2014a. Based on the phenomena in Figure 1, the biological cluster innovation system and innovation institutional governance system in Zhangjiang and Nanchang are relatively close to each other. Besides, the correlation between innovation system and innovation system governance system of Tonghua biomedical cluster is weak. e correlation development of the three biomedical clusters showed a fluctuating state, indicating instability in the correlation development. e positive correlation was relatively high in Nanchang and Zhangjiang biomedical high-tech clusters. Tonghua biomedical cluster was the lowest.
Zhangjiang and Nanchang biomedical clusters had the lowest positive correlation in 2015. e correlation of the Zhang jiang reached its maximum in 2016 while Nanchang had the highest correlation in 2013. In the 7 years of Zhangjiang and Nanchang biomedical clusters, the correlation between the innovation system and the innovation system governance system fluctuated around 0.8. However, the correlation of the Tonghua biomedical cluster fluctuates around −0.2 with a large fluctuation range. Because of the fluctuation of correlation, the dynamic coordination of the innovation system and innovation institutional governance system of the three biomedical clusters has not reached the optimal level. erefore, this paper focused on how to promote the innovation system and innovation institutional governance system to achieve the optimal coordination state. Greater attention was given to the use of adjusting order variables to achieve the optimal state for all parties in Figure 1.

Adding the Test of Order Parameters.
According to pseudocode lines 32, a regulating order parameter was added between the variables of innovation institutional governance system and innovation system. Its values ranged from 0 to 1. Matlab2014a was used to adjust the order parameter. After the actual adjustment of the order parameter test, the optimal coordination state in Figure 2 was obtained. e trend of dynamic coordination was Zhangjiang > Nanchang > Tonghua in 7 years. e correlation degree of the three was more compact, hence indicating an upward trend. After adjustment of order variables, the following mathematical expressions could be obtained in this study: [TongHua, ZhangJiang, NanChang] T � 1.3 −1.
Matrix expression was the order variable intensity to be adjusted for the three biomedical clusters. According to pseudocode lines 47, adjusting the weight of order parameters could promote stability. Tonghua cluster achieved orderly and stably development, which needed to adjust bigger weight value. e order parameter weight adjusted by Mathematical Problems in Engineering Nanchang ranked second, while Zhangjiang needed the least weight value of order parameter. After adjustment, the ranking of cluster development trends was also Zhangjiang > Nanchang > Tonghua. In Figure 2, the positive correlation between Shanghai and Nanchang was between (0.3, 0.5], which belonged to a moderate correlation. is scope indicated that the degree of coordination between Zhangjiang and Nanchang had a certain foundation. e simulation results in Figure 2 showed that coordination states were close to current situation of development of Chinese regional economy. erefore, the optimal development of innovation and governance coordination lays a foundation for the green development of biomedical clusters, which has far-reaching practical significance.

Future Prediction and Discussion.
e synod order parameters set in this study play a role in promoting the development of the current three biomedical clusters. It can be known from pseudocode lines 50 that the correlation of the three biomedical clusters will continue to play a role in the next few years. It is predicted that the collaborative development of the innovation system and innovation institutional governance system can continue to maintain the optimal effect after two years. e details are shown in Figure 3. is effect is very significant for the late catch-up of the Tonghua biomedical cluster. In the ninth year, Tonghua and Nanchang biomedical cluster can be realized in the same echelon. erefore, the innovation system is set as variable A in this paper. en the three variables are A 1 , A 2 , and A 3 , respectively, in the system. Similarly, innovation agency governance system is set as variable B.
en the three variables are B 1 , B 2 , and B 3 , respectively in the system. us the correlation between subsystem A and subsystem B can be expressed as the correlation between each factor. We set A � e specific correlation values of each element of the three biomedical clusters were obtained. According to formula (1), the   was the best element correlation in Zhangjiang biomedical cluster. A 3 B 1 and A 3 B 3 was the best element correlation in Nanchang biomedical cluster. However, there are several cases in which the correlation coefficient of the Tonghua biomedical cluster exceeds 1. is does not conform to the value range of correlation, so the optimal coordination state of the Tonghua biomedical cluster cannot be implemented. erefore, if Tonghua biomedical cluster wants to change the current situation of not achieving optimal synergy, it needs to change the existing innovation and development structure to change the revenue data.

Conclusion and Enlightenment
e level of regional economic development in China is closely related to the quality of the cluster ecosystem. Due to the differences in institutional governance level and innovation capability, the collaborative state of the cluster ecosystem in different regions has significant heterogeneity. As a typical state in the evolution of the cluster ecosystem, the innovation-oriented industrial cluster has become an important driving force of regional innovation. It is led by industry and based on cooperation with universities and research institutes, which provides conditions for the highquality development of the cluster ecosystem.
In the construction of synergistic relationship, innovation and institutional governance influence and interact with each other. us, it plays a positive role in the sustainable development of the cluster ecosystem. Systematic innovation integrates various innovation subjects and elements in the cluster and provides a platform for innovative talents of high-tech enterprises in the cluster ecosystem. In addition, the characteristics of the cluster ecosystem, such as selforganization and openness, make it inseparable from the support of institutional governance, guide the cluster to avoid some risk factors, and realize the improvement of innovation efficiency. e stronger the correlation between innovation system and institutional governance system, the higher the collaborative quality of cluster ecosystem. According to the development data of the three biomedicine clusters, Zhangjiang ranks the highest in synergy quality, Nanchang the second, and Tonghua the last. At the same time, this paper found that Zhangjiang and Nanchang can achieve the best coordination state, but Tonghua cannot. Further analysis shows that there is the highest correlation between the number of R&D personnel and the number of institutions in Zhangjiang. In that regard, Zhangjiang attaches great importance to talent attraction and realizes the coordination between institutional governance and R&D talent attraction within the cluster. Nanchang biomedical cluster attaches importance to the development of high-tech enterprises innovation elements of the "reservoir" function. e system has also issued a considerable level of governance and formed a highly related development environment. Tonghua biomedicine cannot achieve the state of coordinated development. If Tonghua wants to change this state, it needs to change the current institutional governance system and further improve the innovation benefits of the cluster ecosystem. erefore, the correlation between the innovation system and institutional governance system has a direct The time change of the composite system Tonghua Zhangjiang Nanchang    Mathematical Problems in Engineering impact on the synergy level of biomedical clusters. us, it provides a certain reference for promoting the high-quality development of the cluster ecosystem.

Data Availability
e Government Support Fund data used to support the findings of this study have been deposited in the National Bureau of Statistics of China repository (http://www. stats.gov.cn/tjsj/ndsj/). e Identification of High-Tech Enterprises data used to support the findings of this study were supplied by Torch High-Tech Industry Development Center, Ministry of Science and Technology of China, under license and so cannot be made freely available. Requests for access to these data should be made to http:// www.yearbookchina.com, https://www.yearbookchina. com/navibooklist-n3020013200-1.html.
e Innovation Profit data used to support the findings of this study were supplied by Torch High-Tech Industry Development Center, Ministry of Science and Technology of China, under license and so cannot be made freely available. Requests for access to these data should be made to http:// www.yearbookchina.com, https://www.yearbookchina. com/navibooklist-n3020013200-1.html.
e Patent for Invention data used to support the findings of this study were supplied by Torch High-Tech Industry Development Center, Ministry of Science and Technology of China, under license and so cannot be made freely available. Requests for access to these data should be made to http:// www.yearbookchina.com, https://www.yearbookchina. com/navibooklist-n3020013200-1.html.

Conflicts of Interest
e authors declare that they have no conflicts of interest.