4.2.1 Equation of evolution of composite system based on Bertalanffy general system theory.

The coupling process between the high-tech industry and the regional economic subsystems can be expressed through the quantification of the two and their process of interaction. A system coupling process model was constructed by referring to the idea of system evolution in general system theory. The processes of change in the high-tech industrial subsystem and regional economic subsystem are nonlinear, and models of their evolution can be expressed as: (3)

In the formula, f is x_j nonlinear function obtained by Excel fitting (we can judge the reasonableness of the fitting function based on the degree of fit). Because the stability of a nonlinear system depends on the nature of an approximate system feature root [46], under the premise of ensuring the stability of motion, the above nonlinear system was obtained after expanding it in the Taylor series near the origin and omitting the highest order: (4)

te,se represent the total high-tech industry and regional economy subsystems (the indicators in the Table 1), and their relationships are as follows: (5)

In the above formula, x_1j, x_2j represent elements of the high-tech industry and regional economic subsystem, respectively, and w_1j, w_2j represent the weight of each element. According to the Bertalanffy general system theory, the two subsystems form a composite system, and the equation of its evolution can be expressed as: (6)

In the above formula, α₁, α₂ represent the response coefficients of the high-tech industrial subsystem and the regional economic subsystem, respectively, to the evolution of the former. They express the contributions of the state representations of the two subsystems to the rate of evolution of the high-tech industrial subsystem. β₁, β₂ represent the response coefficients of the high-tech industrial subsystem and the regional economic subsystem, respectively, to the evolution of the the latter. They express the contributions of the state representations of the two subsystems to the rate of evolution of the regional economic subsystem. The above parameters indicate the direction and intensity of interactions between the two subsystems, and may all be constant at some stage of system development.

4.2.2 Solving for degree of system coupling based on arctangent function.

In the system, the two subsystems interact. Any change in one causes changes in the entire system. Under these influences, speed of evolution is expressed as: (7)

Because the system contains only two elements f(te) and f(se), when they are coordinated, the entire system is coordinated. The speed of evolution V of the system can be seen as a function of V_A and V_B, and thus V = f(V_A, V_B). Then, we can study the coordinative relationship of the system f(te) and f(se) through changes of V when using V_A and V_B as control variables. Because the regional economic subsystem evolved more quickly than the high-tech industrial subsystem, its trajectory was an ellipse with the following relationship: (8)

In the formula, θ represents the degree of coupling between the subsystems. We can judge the state of evolution of the system and the degree of coupling between the subsystems according to θ. The degree of coupling represents the variation between coordinate quadrants, which is a continuous cycle process. n takes an integer.

In an evolutionary cycle, the entire system underwent four stages: interactive development, system degradation, system collapse, and system regeneration [47].

1. 0° + 2πn ≤ θ < 90° + 2πn indicates that the high-tech industry and the regional economic system developed interactively. θ = 0° + 2πn is the starting point of the high-tech industry and regional economic system coordination. 0° + 2πn < θ < 45° + 2πn indicates the coordinated development of the two systems, θ = 45° + 2πn indicates that the speed of development of the two subsystems is equal, and is the best position for coordinated development. 45° + 2πn < θ < 90° + 2πn indicates that the development of high-tech industries is constrained by regional economic development.
2. 90° + 2πn ≤ θ < 180° + 2πn indicates that the high-tech industry and the regional economic system were in a state of degradation. The regional economic development began to experience negative growth while the development of high-tech industries slowed, and the entropy of the entire system increased.
3. 180° + 2πn ≤ θ < 270° + 2πn indicates that the high-tech industry and regional economic system were in a state of disintegration, and experienced negative growth. θ = 180° + 2πn indicates that the regional economic growth rate was zero. With continuous increase in θ, the negative growth rate of high-tech industries continued to decrease, eventually reaching zero, and the negative regional economic rate of growth increased.
4. 270° + 2πn ≤ θ < 360° + 2πn indicates that the high-tech industry and regional economic system were in the process of regeneration. The high-tech industrial system was beginning to evolve, the economic recession of the regional economic system was subsiding, and they entered a new evolutionary cycle.

4.3.1 Factor detector.

The core idea of the factor detector is to determine whether changes in an environmental factor and a geographical occurrence have significant spatial consistency. If they are consistent, this indicates that the environmental factor is decisive for the occurrence and development of the geographical occurrence.

(9)

q_DU is the impact detection index of the influential factors on the degree of coordination of urbanization and the ecological environment composite system, n is the number of research units, n_D,i is the number of samples of the second-level research unit, m is the number of secondary research units, is the variance of the degree of coordination of the urban agglomeration complex system, and is the variance in the degree of coordination between the subsystems. Assuming , the model is established. The range of values of q_DU is [0,1]. q_DU = 0 indicates that the spatial distribution of the degree of coordination of the composite system was not driven by the influential factors. The larger the value of q_DU was, the greater the influence of the natural factors was on the degree of coordination of the composite system. The different categories of the influence degree (Table 2) were divided referring to the relevant literature [50] and according to the range of influence coefficient.

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Table 2. Classification of impact levels.

https://doi.org/10.1371/journal.pone.0231335.t002

4.3.2 Interaction detector.

The detection of interaction can be used to quantitatively characterize the relationship between the influential factors in terms of the degree of coordination of the composite system. For example, for factors A and B affecting the degree of coordination of the composite system, a new layer C is formed by spatially superimposing A and B. The attributes of C are determined by A and B together. By comparing the influence of layers A and B with that of layer C, the strength of the influence of the interaction of the two factors on the spatial pattern of the degree of coordination of the composite system can be determined (Fig 4).

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Fig 4. Redefined interaction relationships.

https://doi.org/10.1371/journal.pone.0231335.g004

5.1.1 Temporal characteristics.

The total factor productivity reflects the level of efficiency of the technological innovation of high-tech industries, that is, the input–output ratio of innovation in high-tech enterprises. From 2006 to 2016, China’s high-tech industry developed rapidly, the scale of industry expanded, the level of technology improved, and the total factor productivity increased by 37%. Technical efficiency increased by 13.3%, scale efficiency by 3.9%, pure technical efficiency by 9%, and technological progress increased by 20.8%. In recent years, the state has invested significant funds to promote technological innovation. The growth in technological efficiency is the core force driving the growth of the total factor productivity in China’s high-tech industries, and both have exhibited a trend of a “spiral rise.” The improvement in technical efficiency is mainly owing to the increase in pure technical efficiency, which in turn is the result of a rapid improvement in the capability for technological innovation of scientific research institutions and high-tech enterprises. From 2006 to 2011, technical efficiency declined, and technological progress grew rapidly. China’s high-tech industry is an export-oriented economy; due to the financial crisis, technical efficiency decreased, and the crisis awareness of companies has promoted rapid technological improvement. The growth of technological progress has since been slow whereas technical efficiency is growing rapidly. With an emphasis on the high-tech industry in the 12th Five Year Plan and the proposal of the national One Belt, One Road strategy, high-tech industrial technology has been continually optimized and its efficiency improved to yield a snowball effect.

In terms of evolutionary trends, the total factor productivity of China’s high-tech industry showed a composite W-type trend of change, and the other indices followed a wave-like law of evolution from 2006 to 2016. The technological progress index exhibited the largest fluctuation and pure technical efficiency yielded the smallest. Fluctuations in technical efficiency and scale efficiency were moderate, and were consistent (Fig 5). In terms of total factor productivity, except in 2010 and 2014, the DEA state of efficiency (DEA efficiency shows that the index is greater than or equal to one) was achieved in all other years, and peaked in 2011. This is because the national 12th Five Year Plan was officially released in 2011, and called for the development of high-tech industries, which has since enabled the industry to develop at an unprecedented rate. The trends of development of technical and scale efficiency have been highly consistent, and there was high coordination between the efficiency of resource allocation as represented by technical efficiency and the design of the management system as represented by scale efficiency. This indicates that the national incentive and support policies enhance the technical efficiency of the high-technology industry.

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Fig 5. Time series evolution of the efficiency of technological innovation of China’s high-tech industry from 2006 to 2016.

https://doi.org/10.1371/journal.pone.0231335.g005

5.1.2 Spatial characteristics.

There was a significant spatial difference in changes in total factor productivity in high-tech industries, forming a core-edge pattern with the middle and upper reaches of the Yangtze River as the center of concentration. There were eight declines in total factor productivity in the 30 provinces (municipalities, autonomous regions) and 22 rises (Table 3) in 2006–2016. The total factor productivity of economically backward areas, such as the northwestern and northern areas, and regions of Yunnan, economically developed areas such as Jiangsu, Zhejiang, Shanghai, and the southern coastal areas declined significantly. The total factor productivity of the middle and upper reaches of the Yangtze River, the Yellow River Basin, and the three northeastern provinces showed a clear upward trend, with the middle and upper reaches of the Yangtze River rising the most significantly (Fig 6). The decline in total factor productivity in Jiangsu, Zhejiang, Shanghai, and the southern coastal areas stemmed from their lower technical efficiency than the national average (1.008), less than one. The economies were more developed, the technological levels were higher, more technical talent was available, and the conditions for innovation and entrepreneurship were better, but factor input far exceeded other regions, and resource allocation and utilization efficiency was low in the above areas. The decline was due to slower technological progress than the national average (1.043) in the northwest and northern area, and regions of Yunnan. The backwardness of regional transportation and poor economic conditions hindered the development of high-tech industries, with fewer technically qualified people, and scientific and technological activities. It is worth noting that the total factor productivity of high-tech industries in the three northeastern provinces was higher than the national average (1.052). In recent years, the state has launched a revitalization strategy for the old industrial bases in the northeast. The government at all levels has promoted institutional reforms to drive industrial transformation with a focus on large and medium-sized enterprises. The cumulative effect of factor inputs promotes technological advancement in high-tech industries. However, only a comparative advantage in the northeastern region was observed compared with developed regions in eastern China, and there was still a big gap in terms of absolute superiority.

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Fig 6. Spatial distribution of annual average of total factor productivity and its decomposition index for China’s high-tech industry from 2006 to 2016.

https://doi.org/10.1371/journal.pone.0231335.g006

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Table 3. Classification of total factor productivity and its decomposition index for China’s high-tech industry in 2006–2016.

https://doi.org/10.1371/journal.pone.0231335.t003

Changes in the technological efficiency of high-tech industries were generally small, and the regions recording an increase exhibited spatial clusters and distributions, forming a group-band distribution pattern with the middle and upper reaches of the Yangtze River as the center. There were nine declines and 21 rises (Table 3) in the technological efficiency of the 30 provinces (municipalities, autonomous regions). The technological efficiency of the economically backward areas, such as the western, central, southern coastal, and northeastern regions, and economically developed areas, such as Jiangsu, Zhejiang, and Shanghai, declined significantly. The technological efficiency of the middle and upper reaches of the Yangtze River, the upper reaches of the Yellow River, and the Bohai Rim region increased significantly, with the most significant increase in the middle and upper reaches of the Yangtze River (Fig 6). The decline in technical efficiency in the western, central, southern, and northeastern regions was due to the decline in pure technical efficiency, lack of investment in regional technological innovation, lack of technical talent, and a low technical level. Taking Heilongjiang as an example of one of China’s old industrial bases, it lags behind other provinces of China in high-tech industrial technological innovation and lacks technical talent. The decline in technical efficiency was due to a decline in efficiency of scale in Jiangsu, Zhejiang, and Shanghai. That is, investment in high-tech industries was poor, and the allocation and management of resources needs to be improved. The increase in technical efficiency occurred mainly due to an increase in scale efficiency in the middle and upper reaches of the Yangtze River, the upper reaches of the Yellow River, and the Bohai Rim region, especially in the western, central, and northeastern provinces. The government at all levels attached importance to the development of high-tech industries and advocated independent innovation of enterprises, showing a trend of innovation. For these reasons, scale efficiency increased significantly.

5.2.1 Composite system is in state of interactive development except for a few regeneration stages.

The degree of coupling of China’s provincial high-tech industry and regional economic composite system fluctuated in the interval [-15.3, 49.5] from 2006 to 2016, and most values were in the interval [0, 49.5]. That is, the composite system was in a state of interactive development. The high-tech industrial subsystem and regional economic subsystem were both independent and strongly relevant. The two subsystem interacted and evolved at multiple levels and aspects, and a virtuous circle within the composite system was realized based on the synergistic effects of each link, thereby promoting synergy and orderly development among these subsystems.

5.2.2 Degree of coupling of composite systems in provinces showed increasing trend.

The degree of coupling of the composite systems decreased year by year in Heilongjiang and Liaoning provinces, while it showed a wave-like trend of change in Guizhou, Ningxia, Jilin, Zhejiang, and Shanghai, and an increasing trend in the rest of the provinces. The development of high-tech industries remains in a crucial period in the western and northeastern provinces. To achieve the goal of generating income with technology requires that the government invest more resources, and that local enterprises attach importance to technological innovation. In 2016, the composite systems of all provinces were in an interactive state of development, which showed that China’s high-tech industry had developed rapidly, and had a strong synergistic and mutually beneficial synergetic effect on the regional economy.

5.2.3 Degree of coupling of composite system showed spatial pattern of Center > East > West > Northeast.

The average degrees of coupling of composite systems of the China’s four major plates showed a spatial pattern of Center > East > West > Northeast (Fig 7). The eastern coastal areas underwent strong economic development, and had superior scientific and technological talents to other regions. However, the regional economy and the high-tech industries were strongly independent and did not form a good mutual promotion effect. The economic strength and high-tech industry of the central region were disadvantaged compared with those in the eastern region. However, with the support of the country’s central rise policy, the central region quickly developed in science and technology. This led to a strong synergistic effect between the regional economic system and the high-tech industrial system. Under the influence of the western development policy, the western region made significant progress in its regional economy and invested more resources to support the development of local high-tech industries. However, technological diffusion was difficult in the western region, and the cycle of the conversion effect of the high-tech industrial economy was longer than in the other regions. This led to the weak mutual promotion of high-tech industries and regional economies, which restricted their simultaneous development. The synergy between the high-tech industry and the regional economy weakened year by year in the northeast, where the development of the former could not keep up with that in the latter. An old industrial area of China, its traditional industrial technology could not adapt to modern industry, and local enterprises need to quickly import technological knowledge from abroad to promote technological progress and improve technological innovation.

5.3.1 Analysis of factors controlling degree of coupling of China’s provincial complex system.

The five most influential factors for the degree of coupling between China’s provincial complex system were the gross domestic product, efficiency of technological innovation, research and development expenditure, total retail sales of social consumer goods, and the number of high-tech companies. The coefficient of influence was higher than 0.6, and all passed the significant level test of 0.01. The first two significantly affected the degree of coupling of the composite system. Since the reform and opening up, China’s economy has continued to grow at a pace, and the per capita GDP has increased from $156.4 in 1978 to $8826.99 in 2017, 55.44 times higher [51]. The innovation capability of its provinces has also improved significantly. However, there is a wide spatial difference between the eastern and western regions, with a significant Matthew’s effect. Expenditure on research and development has a significant impact on the degree of coupling of composite systems. In recent years, China’s expenditure on this has increased constantly. It ranked second in the world on this measure for the first time in 2013. The gap between the total input in China and the US is decreasing year by year. The intensity of input reached the level of moderately developed countries in 2017. The total retail sales of social consumer goods and number of high-tech enterprises affected the degree of coupling of the composite system. The former reflects the people’s material and cultural living standards as well as the scale of economic market development during the research period. The Chinese economy was dominated by the market supplemented by government intervention. To stimulate domestic demand, the Chinese government strengthened structural reforms of supply and measurement, where the latter reflects the level of scientific and technological development.

5.3.2 Analysis of factors controlling degree of coupling of composite systems in different regions.

The five most influential factors for the degree of coupling of composite systems were efficiency of technical innovation, high-tech product export value, gross domestic product, foreign direct investment, and total retail sales of social consumer goods in the eastern region. Their impact coefficients were all higher than 0.6, and all passed the 0.01 significance level test. The first were most important for the degree of coupling of the composite system. There was confluence of technical talent, perfect transportation construction, and significant scale and cluster effects of high-tech enterprises. Foreign trade developed rapidly in the eastern coastal areas, and the external sales of goods brought advanced foreign technology that promoted innovation. The gross domestic product and foreign direct investment affected the degree of coupling of the composite system. Rapid industrialization accelerated economic development, but has also led to a wide gap between the rich and the poor. In 2015, China utilized a foreign capital of USD 1262.67 trillion, which is the world’s largest foreign investment. It was especially rather large in the eastern region. The total retail sales of social consumer goods also affected the degree of coupling of composite systems. The income of residents has steadily increased, and this supports the increase in the social consumer goods in the eastern region.

The five most influential factors for the degree of coupling of composite system were gross domestic product, efficiency of technological innovation, research and development expenditure, high-tech product export value, and total retail sales of social consumer goods in the central region. Their influence coefficients were higher than 0.6, and all passed the 0.01 significance level test. The gross domestic product had a significant influence on the degree of coupling of composite systems. In recent years, many industries have transferred from the eastern to the central region, and local governments have carried out policy adjustments and institutional innovation to promote economic upgrade and technological innovation. The efficiency of technological innovation, research and development expenditure, and high-tech product export value affect the degree of coupling of composite systems. The resource endowment and industrial foundation region were good in the central areas, government support had improved, and the high-tech industry was consequently developing rapidly. The total retail sales of social consumer goods also affected the degree of coupling of composite systems. The total retail sales of consumer goods is an important part of the GDP, and influences the degree of coordination of the composite system by affecting economic growth.

The five most influential factors for the degree of coupling of composite systems were the number of high-tech companies, number of college students per 10,000, research and development expenditure, number of research and development personnel, and efficiency of technological innovation in the western region. Their influence coefficients were higher than 0.6, and all passed the 0.01 significance level test. The first three strongly affected the degree of coupling of composite systems. The western region had undertaken backward production capacity in the eastern region, but traffic construction was not optimal, educational resources were scarce, and financial support from the government was limited. The number of research and development personnel affected the degree of coupling of composite systems. The delay in educational development led to a lack of technical talent, and few skilled people. The efficiency of technological innovation impacts the degree of coupling of composite systems. Resources are limited, the output of and investment in technological innovation are low, and the efficiency of innovation needs to be further improved in the western areas.

The five most influential factors for the degree of coupling of composite systems were research and development personnel, research and development expenditure, efficiency of technological innovation, gross domestic product, and total retail sales of social consumer goods in the northeast areas. Their impact coefficients are higher than 0.6, and all passed the 0.01 significance level test. The number of research and development personnel significantly affected the degree of coupling of composite systems. The northeastern region had the highest population outflow in China. A large number of technical talents migrated to the Beijing–Tianjin region, resulting in a sharp decline in the number of research and development personnel in the region. Research and development expenditure, efficiency of technological innovation, and gross domestic product also impacted the degree of coupling of composite systems. The national northeast revitalization strategy has led to heavy investment and policy support, but the efficiency of resource allocation remains low, resulting in low efficiency of technological innovation. Affected by the old industrial economic model, the northeastern economy has experienced a significant decline.

5.3.3 Factors analysis of degree of coupling of provincial composite systems.

The interaction of two elements had a greater influence than a single factor on the degree of coupling between technological innovation and the regional economic composite system, indicating that a single factor had a positive influence on the degree of coupling of the composite system, and synergy was strong. Research and development expenditure, and the efficiency of technological innovation had the highest combined impact on the degree of coupling of composite systems, which indicates that the two had the strongest interaction with it. Research and development expenditure significantly enhanced the degree of coupling of composite systems by increasing the scale effect of technological innovation. The efficiency of innovation also significantly enhanced this by promoting the high-quality development of the regional economy. The high-tech product export value, effective invention patents, number of college students per 10,000, and amount of foreign direct investment had nonlinear interactions with the degree of coupling of composite systems, and their interactions were significant. The remaining elements were two-factor enhanced interactions, and the effects were not prominent.