*3.2. Estimation of Parameters*

The regression model was established to estimate the coefficient parameters of variables under the influence of current innovation policies. Innovation performance is a dependent variable, and industrial knowledge absorptive capacity and academic knowledge transfer capacity are independent variables. In this paper, the average number of observation indicators is taken as a comprehensive level of relevant variables.

The regression result shows that the influence coefficient of industrial absorptive capacity on the performance of collaborative innovation is 0.675, meanwhile, the influence coefficient of academic knowledge transferability is only 0.356. Under current innovation policy, it seems certain that industrial absorptive capacity plays a more important role than the academic knowledge transfer capability during the process of collaboration between industry and academia (0.675 > 0.356) (See Table 3 for details). Considering the survey that the industrial incentive policy is lower than the enterprise's expectation, it seems to get a hypothesis that the future innovation policy should focus more on the industrial incentive policy in China. Therefore, we further explore the evolutional mechanism when innovation policy changed using the simulation model to test this hypothesis.


**Table 3.** Result of regression analysis.

Note: the figures in the table are estimated values of parameters, and the values in brackets are estimated standard errors. \*\*\* means significant at the level of 0.01, \*\* means significant at the level of 0.05, \* means significant at the level of 0.10 (bilateral test).

#### *3.3. Model Selection*

**Model selection**. The Belousov-Zhabotinsky's (BZ) reaction is an experimentally accessible example of chemical self-organization [44,45]. In the 1970s, nonlinear oscillations and bifurcations were discovered first by modelling and then by experiments for the autocatalytic Brusselators and the BZ chemical reaction [46]. The autocatalytic chemical reaction phenomenon plays a vital role in the breakdown of the stability of the thermodynamics. Self-organization phenomena, leading to ordered behavior, can arise in an initially uniform and time-independent system far from equilibrium. Their interest arises primarily from the fact that the emergence of order is often accompanied by the appearance of spatially asymmetric patterns. Such symmetry breaking phenomena are therefore of special interest in modeling the behavior of complex objects, where both order and asymmetry are ubiquitous [47].

The self-organized pattern formation of non-linear complex systems has very useful applications in many fields of social science as well. In China, Brusselator model was firstly taken by Li as the judgment tool of dissipative structure threshold [48], Li et al. studied the evolutionary mechanism of industry and university alliance based on 2-D system dynamic equation [49], Zhang et al. built the 3-D variable model to introduce "BZ" reaction for studying the evolutional mechanism of the enterprise system [50]. In this work, we use the 3-D variable model to explore university-industry-government relations in the national system of innovation.

A class of problems for which system self-organizing has been particularly well studied is described by the so-called BZ reaction equations [51]. BZ reaction is the typical system with self-organization property. It specifically refers that the chemical oscillation phenomenon occurs when citric acid is oxidized by potassium bromate under the acidic conditions with metal cerium ion as catalyst, and furthermore, certain rhythmicity in time also exists there, namely, color rectilinear oscillation occurs in the solution between achromatic color and faint yellow. According to Prigogine's explanation of the oscillating reaction: when the system is far away from the equilibrium state, namely, nonequilibrium nonlinear region, unordered even state is not always stable [52]. Under the specific dynamic conditions, unordered even stationary state can be out of stability and generates time-space ordered new status. At the microscopic scale, it seems unordered that microscopic particles of various reacting matters make random motions and collisions, but at the macro level, the reaction is ordered in both space and time.

The system variables can be divided into fast and slow variables, and the slaving principle is found by the synergistic theory [52], namely, slow variable dominates the progress and result of the system evolution and development, under the condition of threshold value, such slow variable becomes the dominant variable, and other variable becomes slaving variable. The slaving principle in the self-organization synergy theory provides the possibility for the establishment of the simulation equation to study the dynamical mechanism of the TH synergy in national system of innovation.

**Feasibility analysis**. The innovative dynamics are endogenized and the relations among the agents reconstructed by the dynamics of innovations [10]. In other words, the innovation system is a self-organizing system. Prigogine noted that a synergistic self-organizing system must also possess four general conditions: far from equilibrium, openness, nonlinear interactions and fluctuation [53]. Using self-organizing synergy theory as a research fulcrum, it should be confirmed that national system of innovation meets all prerequisites of a synergetic self-organizing system.

The national innovation system has the attributes of synergetic self-organizing system: (1) Open innovation theory proposed by Chesbrough shows that openness is the important prerequisite and approach to improve innovation performance, the opening degree between system innovative actors directly decides the effect of performance of innovation [54]. In the network-based and knowledge-based economy, the innovation system has evolved into an open era from the traditional closed standalone pattern, and furthermore, the university-industry-government linkage becomes the core of the national open innovation system. The process of industry-university collaborative innovation is the knowledge-core value innovation process for information sharing, knowledge production, knowledge spread and application [55]. Therefore, Haken points out that it is more suitable for replacing thermodynamic entropy into information entropy for understanding the nonequilibrium social systems [56]. (2) Christensen considers that innovation is divided into incremental innovation and disruptive innovation, and the different fluctuation rules are revealed in the innovation process [57]. (3) The concept of knowledge transfer has been proposed by many scholars while studying asymmetric knowledge distribution [58]. Cohen and Levinthal reveal the vital role of the absorptive capacity in knowledge transfer [59], and subsequently explorative and exploitive organizational study are proposed by March [60] to deepen the connotation of organizational absorptive capacity. Above all, it is obvious that NSI meets all the preconditions of the self-organizing synergistic system to apply B-Z reaction for the simulation study.

#### *3.4. Model Building*

The synergistic theory, namely system variable, is divided into fast and slow variables [29]. It is referenced to explore the slaving principle that slow variable dominates the development course and result of the system evolution. Following literature reviews and empirical research above, three key variables of national system of innovation had been refined which are: the academic knowledge transfer capability, the industrial knowledge absorptive capacity, and finally the performance of innovation. However, how the national system of innovation will gradually progress was still unknown when innovation policy context or capabilities change. This paper builds a three-D equation set based on BZ reaction, to explore the dynamic mechanism of TH when innovation variables change over time.

**Dynamic evolution equation of industrial knowledge absorptive capacity**. Under the original state of academia and industry linkage, explicit knowledge transfer is given priority. While the proportion of the tacit knowledge increases overtime, firms may fail to improve absorptive capacity synchronously and academic researchers may be limited by their knowledge interpretation and dissemination abilities, the knowledge transfer becomes more difficult. In addition, it is obvious that innovation performance is always influenced by incentive policy. Therefore, under the certain condition of incentive policy θ, logistic evolution equation of state variable of industrial knowledge absorptive capacity is as follows:

$$\frac{1}{\alpha} \frac{d\mathbf{x}\_1}{dt} = \theta \mathbf{x}\_1 + \theta \frac{\beta}{\alpha} \mathbf{x}\_2 + \gamma \mathbf{x}\_1 \mathbf{x}\_3 \tag{1}$$

In which, θ*x*<sup>1</sup> is the autocatalytic factor under the incentive policy context, θ reflects the role of innovation policy to *<sup>x</sup>*1. <sup>θ</sup><sup>β</sup> <sup>α</sup> *<sup>x</sup>*<sup>2</sup> is the impact factor of *<sup>x</sup>*<sup>2</sup> on *<sup>x</sup>*<sup>1</sup> under incentive policy context <sup>θ</sup>, <sup>β</sup> <sup>α</sup> is influence coefficient. HEIs and PRIs' knowledge transfer promotes the enhancement of firms' absorptive capacity. γ*x*1*x*<sup>3</sup> shows the feedback influence of innovation performance *x*<sup>3</sup> on *x*1, the endogenous promotion of enterprises' innovation performance will act on more research input of enterprises and enhance their technology capabilities, which weakly depends on whether it is driven by policy.

**Dynamic evolution equations of academic knowledge transfer capability**. In an initial state, HEIs and PRIs are the important knowledge sources for the industry to improve technology capabilities and innovation performance in the knowledge-based economy. Academic knowledge transfer capability is influenced by both industrial absorptive capability and innovation performance in the evolutional process. Therefore, under the certain condition of incentive policy θ, logistic evolution equation of academic knowledge transferability is as follows:

$$\frac{1}{\beta} \frac{d\mathbf{x}\_2}{dt} = -\theta \mathbf{x}\_2 - a\mathbf{x}\_1 \mathbf{x}\_2 + \frac{\mathcal{V}}{\beta} \mathbf{x}\_3 \tag{2}$$

In which, −θ*x*<sup>2</sup> means the autocatalytic factor of *x*<sup>2</sup> under incentive policy. Its coefficient is negative, showing that with the constant improvement of academic knowledge transfer capability in HEIs and PRIs, marginal income decreases progressively because HEIs or PRIs fall into the dilemma situation: focusing on knowledge production or knowledge commercialization under their limited resource conditions and time. −α*x*1*x*<sup>2</sup> shows the influence factor of *x*<sup>1</sup> on *x*2, under assured incentive policy θ. The enterprise is also faced up with the difficult choices: enhancement of R&D or improvement of absorptive capability. <sup>γ</sup> <sup>β</sup> *x*<sup>3</sup> is the influence factor of collaborative innovation performance on academic knowledge transfer capability there exists positive incentive effect of the promotion of innovation performance on academic knowledge transfer capability, and <sup>γ</sup> <sup>β</sup> is the influence coefficient.

**Dynamic evolution equation of collaborative innovation performance**. The purpose of innovation in the industry is to finally achieve commercial successes by means of open absorption and utilization of heterogeneity knowledge. So collaborative innovation performance is essentially only related to its own state level of absorptive capability of firms. Therefore, under the certain condition of incentive policy θ, logistic evolution equation of state variable is as follows:

$$\frac{1}{\mathcal{V}}\frac{d\mathbf{x}\_3}{dt} = \eta\_1 \mathbf{x}\_3 + \eta\_2 \theta \frac{\alpha}{\mathcal{V}} \mathbf{x}\_1 \tag{3}$$

In which, η1*x*<sup>3</sup> is the autocatalytic factor of collaborative innovation performance, the pressure of market competition and endogenous innovation dynamics make the state of innovation performance in the rising trend. η<sup>1</sup> is constant normally. η2θ<sup>α</sup> <sup>γ</sup> *x*<sup>1</sup> is the impact factor of absorptive capability on the performance of collaborative innovation. The external incentive policy acts on the collaborative innovation performance via absorptive capability finally, embodying that with the improvement of absorbing ability, collaborative innovation performance promotes. <sup>α</sup> <sup>γ</sup> is the influence coefficient, η<sup>2</sup> is constant. Generally, η<sup>2</sup> is normally more than 1, embodying the synergistic effect of industry-university linkage. The reason why the knowledge transfer variable *x*<sup>2</sup> is not included in the equation is that the collaborative innovation performance is finally reflected in the enterprise's innovation performance. The direct impact mechanism of academic knowledge transfer on innovation performance is not clear. η<sup>1</sup> = 2 is supposed in this paper, which reflects that the endogenous power of industry-university linkage promotes the innovation performance, showing the Matthew Effect. If η<sup>1</sup> = 2, it reflects that the innovation performance is multiplied by the synergistic effect of TH under the condition that innovation performance is promoted by absorbing capability.

**Dynamic evolution equations of TH synergy**. Combining the above three equations, this paper constructs the following dynamic evolution equations of TH synergy:

$$\begin{cases} \frac{1}{a}\frac{dx\_1}{dt} = \theta \mathbf{x}\_1 + \theta \frac{\beta}{a} \mathbf{x}\_2 + \gamma \mathbf{x}\_1 \mathbf{x}\_3\\ \frac{1}{\beta}\frac{dx\_2}{dt} = -\theta \mathbf{x}\_2 - a \mathbf{x}\_1 \mathbf{x}\_2 + \frac{\mathcal{V}}{\beta} \mathbf{x}\_3\\ \frac{1}{\gamma}\frac{dx\_3}{dt} = \eta\_1 \mathbf{x}\_3 + \eta\_2 \theta \frac{\mathbf{a}}{\gamma} \mathbf{x}\_1 \end{cases} \tag{4}$$

#### **4. Simulation Results**

In this paper, it is set that in the differential equation, the initial state of the three variables of industrial absorptive capacity, academic knowledge transfer and collaborative innovation performance is X0 = [x1, x2, x3]. The x1, x2, x3 respectively represent the input condition of the three factors of TH statuses before collaboration. At the same time, being specific to the incentive effect generated by external policy environment, there are two conditions divided in this paper: (1) Set the control variable incentive policy θ = 1, it reflects normal support of the country and regional government to the collaborative innovation, the implementation of collaborative innovation under spontaneous condition; (2) set control variable incentive policy θ = 2, it reflects that the country and region give stronger policy support to collaborative innovation, by means of offering necessary infrastructure input, talent input, innovation service support and other incentive mechanism to carry out collaborative innovation, so as to push the implementation of collaborative innovation activities.

It is also specific in this paper to two states of Triple Helix, based on MATLAB simulation analysis software, the studies will be respectively implemented: (1) The ideal status when absorptive capacity and transfer ability are at higher level symmetry, the TH synergy mechanism under two different incentive policy contexts are simulated. (2) The second status is under the current condition in China based on empirical statistical data studied ahead.

#### *4.1. Simulation When Capabilities Balance between Industry and Academia*

Under the balanced condition of absorptive capacity in industry and knowledge transfer capability in academica, we suppose that the performance of collaborative innovation relies on the further implementation of collaborative linkage. Therefore, it is respectively defined that industrial absorptive capacity is 1, academic knowledge transfer ability of is 1 and collaborative innovation performance is 0 (due to certain time delay) for the initial state of the simulation. Namely, under initial state X0 = [1, 1, 0], the study is respectively implemented according to the two conditions of normal incentive policy (θ = 1) and strong incentive policy (θ = 2).

**Normal incentive policy context**. The simulation result of dynamic mechanism in NSI under normal incentive environment (θ = 1) is shown in Figure 2, y1 is industrial absorptive capacity, y2 is academic knowledge transfer capability and y3 is collaborative innovation performance.

**Figure 2.** Dynamic evolution mechanism under the normal incentive policy.

Simulation results: Under the condition of normal external incentive policy context, when x rises to 2, innovation performance is close to 5. The rapid promotion of collaborative innovation performance appears, and absorptive capability is improved rapidly at the same time, and the academic knowledge transfer ability of colleges and universities maintains stable and rises slowly.

Result analysis: (1) Under the condition of weak external incentive policy, because of the comparative matching of knowledge supply capability and knowledge absorptive capability, heterogeneous knowledge accumulated by universities has become the main target for enterprises to absorb, which has rapidly improved the innovation ability and innovation performance of enterprises. (2) In the initial stage, the participation of agents in HEIs and PRIs in collaborative innovation projects has spent a lot of energy, and academic productivity has been affected to a certain extent. (3) The result of long-term interaction between university and enterprises respectively promote their technology capabilities from collaboration.

**Stroger incentive policy context**. The simulation results of the collaborative innovation mechanism under a strong incentive environment (θ = 2) is shown in Figure 3.

**Figure 3.** Ideal dynamic mechanism of NSI with stronger incentive policy.

Research results: Under the ideal condition of stronger incentive policy, industrial absorptive capacity, academic knowledge transfer ability and collaborative innovation performance show the same variation trend with the normal incentive policy, but collaborative innovation performance gets the rapid promotion. Under the condition of x = 2, innovation performance is 19, which is 4 times of the normal incentive policy. At the same time, the absorptive ability is improved synchronously, and knowledge transfer capability shows the secular change trend of firstly dropping and then rising.

Result analysis: The result proves that national or regional innovation policy has the positive effect of promoting absorbing ability and innovation performance when the capabilities of agents match in NSI. It might be four reasons: (1) Innovation policy fosters consensus of synergistic innovation, which reduces the cost of technology transaction. (2) Innovation policy increases investment in innovation infrastructure and enterprise innovation resources, which promote the motive force and capability of synergistic innovation in industry. (3) Innovation policies have increased investment in innovative resources such as university human resources and research funds, which better balance the relationship between innovative services and scientific research. (4) HEIs and PRIs learned heterogeneous knowledge from the industry which promoted the continuous improvement of academic research abilities over time, also strengthened their motivation to participate in collaborative innovation activities for knowledge commercialization.

#### *4.2. Simulation Based on Current Situation in China*

According to the empirical results ahead the influence coefficient of industrial absorptive capability on innovation performance is 0.675, while the influence coefficient of unit knowledge transfer ability to innovation performance is 0.356. Based on the results of the questionnaire, the evaluation of innovation policy by the industry is in the middle level. Therefore, this paper sets the influence coefficient of incentive policy on the performance of collaborative innovation is 1.166. It is confirmed that initial state X0 = [0.675, 0.356, 0] to obtain simulation result of Figure 4. In which, y1 is industrial absorptive capacity, y2 is knowledge transfer ability of HEIs and y3 is collaborative innovation performance.

**Figure 4.** Dynamic mechanism of TH synergy in China.

**Simulation results**: Under the current situation of NSI in china, the synergy of TH is still far from optimal. However, innovation performance is slightly higher than 4 if x = 2, and innovation performance starts to show rapid growth trend, may up to 14, if x = 3. Absorptive capability in industry is in high correlation with innovation performance with system evolution and time advance. Knowledge transfer ability of HEIs and PRIs slowly rises, while the evolutionary trend is stable. The result shows that China's national system of innovation has good prospects for development, and innovation performance will face a significant growth trend over time. (1) In the current situation, the absorptive capacity in industry has exceeded the ability of knowledge transfer of HEIs and PRIs, and it has become the main driving force to promote innovation and development. (2) At present, the level of absorptive capacity has been higher than the level of innovation performance. From the analysis of the evolution progress viewpoint, the role of absorptive capacity and innovative capacity in industry will be gradually revealed, which will sustainably and rapidly improve the innovation performance of national innovation system in future.

**Results analysis**: (1) while the breadth and depth of open innovation have been continuously expanded, industrial absorptive capacity has become the core competence of collaborative innovation. This result elaborates that industrial absorptive capacity is highly correlated with TH synergy. If the absorptive capacity in industry is insufficient, the efficiency of knowledge transfer will also be affected prominently. Not only the cooperation cycle between university and industry becomes long and tough, but also the important and limited resources may be exhausted. When the industrial absorptive capacity matches the academic knowledge transfer capability, the performance of collaborative innovation and the quality of national innovative ecology can be significantly improved. Above all, the industrial absorptive capability plays an important role in TH synergy in NSI. However, while the improvement of industrial capability, the problem of knowledge sharing within the organization is particularly prominent. On the one hand, with the increase of the mobility of enterprises' technical personnel, setting up technical firewalls has become the main strategy of personnel which limits the sharing of knowledge; On the other hand, enterprises still do not pay much attention to knowledge management, which also greatly affects knowledge sharing in the team and organization level. (2) Knowledge transfer capability of HEIs and PRIs shows relative stability. Based on the synergistic theory, the evolution of the system is dominated by slow variables. The knowledge transfer capability of HEIs and PRIs has obviously become the dominant variable that affects triple helix's synergy. In other words, the capabilities of useful knowledge generation, knowledge interpretation and dissemination, already become a bottleneck problem in NSI of China. Evidence also found that with the enhancement of the industrial absorptive capacity, Chinese enterprises are more willing to acquire technology through international merger or global cooperation than local collaborations, which affects the cooperation of domestic universities negatively [61]. With the continuous support of national scientific research investment, universities and scientific research institutions have published many high-quality papers

and applied for a large number of patents, but obviously there is a gap between the knowledge demand of real innovation context and supply from the HEIs and PRIs.

#### **5. Conclusions**

Based on BZ reaction model in non-linear complex systems and MATLAB simulation analysis software, this work introduces a new simulating method to explore the synergistic mechanisms of TH in NSI, and obtained an important conclusions: The hypothesis that the future innovation policy should mainly focus more on the industrial incentive policy in China might not be comprehensive. Innovation policy plays a positive role in promoting the collaborative innovation capability and performance in NSI, and policy objectives need to be targeted at solving bottleneck problem at priority. At present, innovation policy in China faces a dilemma, that is, to continuously increase governmental direct investment in basic and applied research to improve knowledge supply capacity, or to incentive industrial investment to improve knowledge integration and application capacity.

Based on the results of empirical research and simulation research, this paper considers that the domestic academic knowledge capacity is the order variable which dominant the evolution of TH in Chinese NSI. Optimizing governmental direct R&D investment mechanism should be the top priority, especially the application research project funding which accounts for a very high proportion. Although the main goal of applied research projects funding is to promote technology commercialization, the current criteria for competition are mainly composed of published papers, applied patents and previous project experience. Therefore, in order to obtain more governmental funding supports, researchers both in academia and in industry inevitably spend much more time and energy in publishing papers or applying for patents, and ultimately have no energy and motivation to implement commercialization.

Additionally, the incentive policies to encourage industrial innovation investment also need to be further subdivided. In addition to increasing the R&D investment efficiency of state-owned enterprises, how to eliminate the barriers between knowledge production and knowledge circulation may be the key issue of industrial innovation policy. Although the construction of intellectual property regimes has been paid more and more attention to for a long time, and the intellectual property courts also be constructed as a policy innovation pilot, the implementation process of intellectual property regimes is plagued by problems, such as difficult to obtain infringement evidence and the lack of enough supervisors, etc. Most private enterprises prefer to choose management measures to avoid R&D investment or to acquire oversea knowledge by means of strict internal prevention of knowledge sharing, in order to reduce the externality of knowledge spillover. So, optimizing the enforcement mechanism of the intellectual property regimes may also be the key link to eliminate the bottleneck of collaborative innovation.

In summary, if the innovation policy can be more targeted at the upgrading of the domestic supply capacity of useful knowledge in HEIs and PRIs as optimization objectives, at the same time continue to strengthen the implementation of the intellectual property protection regimes, the synergy quality of national innovation system in China would be continually improved, and the endogenous innovation performance would be accelerated rapidly.

**Author Contributions:** It should be noted that the whole work was accomplished by the authors collaboratively. Both authors read and approved the final manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China under the Grant No. 71573222, by the National Education Sciences Planning under the Grant No. BIA150117, by the Natural Science Foundation of Zhejiang province under the Grant No. LZ16G030002, and by the fundamental Research Funds for the Central Universities, by the new type key thinking tank of Zhejiang province "Research institute of regulation and public policy".

**Conflicts of Interest:** The authors declare no conflict of interest.
