In recent years, the global push for green development and carbon neutrality goals has positioned the electric car industry as a pivotal domain for industrial upgrading. Governments worldwide, including China’s State Council with its “New Energy Vehicle Industry Development Plan (2021–2035),” emphasize the necessity of deep integration between the industrial chain and innovation chain to overcome key technological bottlenecks. However, the electric car sector still grapples with issues like immature core technologies and low synergy efficiency in the industrial chain. The fusion network formed by the industrial and innovation chains of electric cars involves multiple heterogeneous nodes, where disturbances in any factor can significantly impact the network, making it a typical complex system. Understanding how to achieve technological breakthroughs and industrial efficiency through “dual-chain” collaboration has become a central topic in academia and industry.
Existing empirical studies on dual-chain integration primarily focus on spatial spillover effects, synergy efficiency, key node identification, and policy drivers. For instance, some researchers have used spatial Dubin models to verify the spatial spillover effects of dual-chain integration on green innovation, finding that policy support can enhance cross-regional technology diffusion efficiency by 15%–20%. Others employed social network analysis (SNA) to construct collaborative industrial chain innovation networks, validating the acceleration effect of upstream-downstream connections on innovation implementation. In Shaanxi Province, policy-guided studies confirmed that dual-chain integration requires technology-sharing platforms to break resource barriers between the innovation and industrial chains. Additionally, research on emerging industries showed that regional venture capital optimizes the input end of the innovation chain, achieving synergistic growth in patent numbers and market value. Case analyses indicate that policies integrating innovation resources in the industrial chain can overcome bottlenecks like insufficient corporate influence and talent shortages, increasing collaborative innovation efficiency by 28%. Digital economy policies, through enhancing the “technology push” of the innovation chain, indirectly drive the integration of the industrial and innovation chains. Furthermore, studies on technological innovation networks reveal that structural embedding by large enterprises can lead to network fragmentation, while industrial chain enterprises’ structural embedding enhances network stability. However, most empirical research remains limited to statistical descriptions of cooperative relationships, lacking systematic modeling. The impact of heterogeneous nodes’ capability differences—such as research institutions having strong innovation but weak industrialization capabilities, and manufacturing firms having strong industrialization but weak innovation capabilities—on network evolution remains unquantified.
From a complex network perspective, scholars have explored dual-chain integration through various lenses. For example, exponential random graph models have been used to quantify the connection preferences among enterprises, universities, and research institutes, showing that differences in entity types between the industrial and innovation chains improve the stability of cooperative relationships. Hierarchical supply chain network dynamic evolution models have revealed the “lifecycle effect” of node exits during the transformation of the electric car industry chain, where node survival time is significantly positively correlated with technological innovation capability (p < 0.05). Edge benefit indicators introduced into electric car industrial chain networks have shown that high-benefit edge clustering accelerates technology diffusion, but these studies often overlook the technology empowerment effect of innovation chain nodes on industrial chain nodes and the impact of dynamic elimination of inefficient nodes on network efficiency. Policy-driven analyses highlight the significant influence of subsidies and standards on the dynamic adaptation of dual chains. Nevertheless, research on the evolutionary modeling of the integration network between the industrial and innovation chains for electric cars is scarce. Some studies have built “network of networks” type innovation networks for the electric car industry, quantifying the synergy of upstream, midstream, and downstream sub-networks through composite system coordination degree models, finding that dependent edges reduce system disorder. However, they do not deeply analyze the synergistic adaptation mechanism of heterogeneous nodes in the fusion network. Others have constructed electric car supply chain networks from a complex network perspective, identifying scale-free and small-world characteristics, but these focus solely on the industrial chain without incorporating the technology spillover effects of innovation chain nodes or dynamically simulating real-time node addition and elimination.
This paper addresses these gaps by constructing a policy-driven dynamic evolution model for the dual-chain integration of electric cars based on complex network theory. The model distinguishes between four types of industrial nodes (raw materials, core components, manufacturers, charging and aftermarket services) and three types of innovation nodes (universities, research institutes, innovation platforms), capturing capability differences through “innovation index–industrial index” dimensions to simulate the synergistic logic of cross-chain “technology supply–demand traction.” A “preferential attachment rule” and “competitive elimination mechanism” are introduced to quantify the combined effects of technological competition and policy drive. Macro and micro policy coefficients are set, and simulations reveal the nonlinear driving effects of policies on network scale and integration degree. Model error rates are validated using multi-regional data, providing a new theoretical framework for understanding the synergistic evolution of industrial and innovation chains and offering actionable strategies for policymakers and enterprises.
The electric car dual-chain integration network exhibits several evolutionary characteristics: policy-driven nature, where multi-dimensional policies accelerate technology transformation and industrial upgrading, forming a “policy-innovation-industry” synergistic closed loop; dynamic openness, with nodes from fields like intelligent networking and cloud computing flowing dynamically due to technological iterations and market uncertainties, ensuring network adaptability; hierarchical heterogeneity, where upstream raw material enterprises focus on technological breakthroughs, downstream manufacturers emphasize规模化 production and market response, innovation chain entities like universities concentrate on basic R&D, and platforms偏向 application transformation, creating a gradient distribution of “strong innovation–weak industrialization” and “strong industrialization–weak innovation” that enables complementary capabilities and synergistic adaptation; ecological integration, where innovation serves as the core link covering the entire lifecycle from R&D to service, with the innovation chain driving industrial chain development through breakthroughs and industrial demand spurring innovation chain upgrades; and connection preferences, where industrial nodes prefer连接 to high-industrialization-capability nodes for supply chain stability, innovation nodes prefer连接 to high-innovation-capability entities for technology diffusion, and cross-chain connections see industrial ends preferring high-innovation nodes and innovation ends preferring high-industrialization nodes.
Compared to existing network models, this model incorporates node type differentiation, macro and micro policy coefficients, dynamic elimination mechanisms, preferential attachment rules, and integration degree metrics, as summarized in Table 1.
| Comparison Dimension | Existing Representative Models | This Model |
|---|---|---|
| Node Coverage | Only industrial chain nodes (e.g., supply chain networks without innovation chain) | 4 industrial node types and 3 innovation node types |
| Policy Drive Design | Qualitative analysis without quantified policy indicators | Introduction of macro policy G and micro policy g coefficients, with competitive elimination rules |
| Dynamic Evolution Mechanism | Static analysis of sub-network features without dynamic node representation | Dynamic preferential attachment based on threshold H, bidirectional connections between innovation and industrial chains |
| Integration Synergy Definition | No cross-chain indicators; focuses on topological features | Integration degree = cross-chain connections / total connections |
| Empirical Validation Scope | Single-region data or no empirical validation | Long-term data validation from multiple regions (e.g., Shaanxi, Yangtze River Delta, Pearl River Delta) |
In the model, nodes are abstracted as follows: industrial nodes include raw material suppliers (e.g., high-energy-density battery providers), core component suppliers (e.g., traditional motor enterprises, balanced capability automotive firms, specialized electric motor developers), manufacturers (e.g.,整车 assembly plants), and charging and aftermarket service points (e.g., fast-charging technology providers, general service nodes). Innovation nodes comprise universities, research institutes, and innovation platforms. Each node is characterized by an innovation index $\alpha_i$ and an industrial index $\beta_i$, both ranging between 0 and 1, generated from normal distributions to reflect real-world capability distributions. Additional parameters include node importance $\tau_i$ (based on betweenness centrality), openness $\lambda_i$ (based on degree), and age $Y_i$. Policy influences are captured by a macro policy coefficient $G$ (uniformly distributed in (0,1)) and micro policy coefficients $g^D$, $g^S$, $g^M$, $g^E$, $g^U$ for each node type (normally distributed in (0,1)).
The evolution rules are structured in steps. Initially, at time step $T=0$, the network has 15 nodes: 2 manufacturers ($M_1, M_2$), 3 core components ($S_1, S_2, S_3$), 4 raw materials ($D_1, D_2, D_3, D_4$), 4 aftermarket services ($E_1, E_2, E_3, E_4$), and 2 innovation nodes ($U_1, U_2$). The initial topology is shown in the figure, with edges representing supply-demand or cooperative relationships. At each time step, new nodes are generated based on innovation nodes and policy-driven probabilities. For an innovation node $U_i$, a new node type is determined by a threshold $H$ calculated as:
$$H = \alpha_{U_i} \cdot \beta_{U_i} \cdot \lambda_{U_i} \cdot \tau_{U_i} \cdot (1 – Y_{U_i}^{-1})$$
where $H$ partitions define node types: if $0 < H \leq H_1$ (e.g., $H_1=0.38$), an innovation node is generated; if $H_1 < H \leq H_2$ ($H_2=0.46$), a raw material node; if $H_2 < H \leq H_3$ ($H_3=0.57$), an aftermarket service node; if $H_3 < H \leq H_4$ ($H_4=0.64$), a core component node; and if $H_4 < H < 1$, a manufacturer node. These thresholds are derived from empirical data to match real-world node distributions. Concurrently, for each industrial node type, the probability of generating an innovation node $P_{ic,U}^*$ or industrial node $P_{ic,I}^*$ is given by:
$$P_{ic,U}^* = \frac{1}{1 + \exp(-\theta \cdot G \cdot g \cdot Y_i \cdot \alpha_i \cdot \lambda_i)}$$
$$P_{ic,I}^* = \frac{1}{1 + \exp(-\theta \cdot G \cdot g \cdot Y_i \cdot \beta_i \cdot \lambda_i)}$$
where $\theta$ is a decay coefficient. New nodes are added to the network with preferential attachment. For an innovation node $U_i$, the probability of connecting to an industrial node $I_i$ is:
$$P_{U_i,I_i}^l = G \cdot g^U \cdot \tau_{I_i} \cdot \lambda_{I_i} \cdot \beta_{I_i} \cdot \alpha_{I_i}^{-1}$$
For an industrial node $I_i$, the connection probability to other nodes $J_j$ is:
$$P_{I_i,J_j}^l = G \cdot g^I \cdot \tau_{J_j} \cdot \lambda_{J_j} \cdot \beta_{J_j}$$
with $g^I$ specific to the node type (e.g., $g^D$ for raw materials). Cross-chain connection probability is defined as the maximum of the two probabilities. Finally, a competitive elimination mechanism removes the weakest node in each type based on competitive intensity $Q_i$:
$$Q_i = \lambda_i \cdot \beta_i \cdot \tau_i \cdot \alpha_i \cdot Y_i^{-1}$$
where nodes with the lowest $Q_i$ in their category are removed at each time step.
To analyze the model, 12 experimental schemes are designed, categorized by macro policy coefficient $G$ ranges: (0.0,0.4), (0.4,0.7), and (0.7,1.0). Within each range, four schemes vary innovation indices $\alpha_i$, industrial indices $\beta_i$, and micro policy coefficients $g$ from low to high. For example, in the $G \in (0.0,0.4)$ range, Scheme 1 has $\alpha_i$ and $\beta_i$ at low values (e.g., $\alpha_{D_i} \in (0.0,0.4)$, $\beta_{D_i} \in (0.1,0.4)$), while Scheme 4 has high values (e.g., $\alpha_{D_i} \in (0.3,0.7)$, $\beta_{D_i} \in (0.4,0.7)$). Simulations are run for $T=500$ time steps, with 10 independent runs averaged for analysis.
Simulation results show that the network degree distribution follows a power-law, confirming scale-free characteristics. The cumulative degree distribution in log-log coordinates has power-law exponents $\alpha$ ranging from 1.426 to 1.478 across schemes, with $\alpha$ decreasing as $\alpha_i$ and $\beta_i$ increase. Betweenness centrality analysis reveals that most nodes have low betweenness (concentrated in [0,0.05]), indicating that few nodes act as hubs. The average clustering coefficient $R_j$ increases with $\alpha_i$ and $\beta_i$, from 0.011 in Scheme 1 to 0.019 in Scheme 4, suggesting a denser network. Global efficiency $R_e$, defined as the average inverse shortest path length, improves over time, with Scheme 1 showing a 19% increase from $T=100$ to $T=500$, and higher $\alpha_i$ and $\beta_i$ leading to greater $R_e$. The average shortest path length $R_l$ decreases over time, with Scheme 1 experiencing an 8% reduction and Scheme 4 a 4% reduction, indicating enhanced connectivity. Integration degree $R_n$, the ratio of cross-chain connections to total connections, rises significantly, from 31% in Scheme 1 to 46% in Scheme 4 at $T=500$, demonstrating stronger dual-chain synergy.
Policy impact is profound. For schemes with low $\alpha_i$ and $\beta_i$, increasing $G$ from (0.0,0.4) to (0.7,1.0) (comparing Scheme 1, 5, and 9) boosts average degree by 17%, global efficiency by 29%, and integration degree by 25%, while reducing average shortest path length by 3%. For high-capability schemes (Scheme 4, 8, 12), the same $G$ increase raises average degree by 15%, global efficiency by 26%, and integration degree by 22%, with a 2% reduction in path length. Micro policy coefficients $g$ also play a crucial role; a 0.1 increase in $g$ can lead to a 15% rise in cross-chain connections. Robustness analysis under random attacks (5% node removal) shows a 13% decrease in global efficiency and a 32% drop in the largest connected subgraph rate, indicating sensitivity to disruptions.
Empirical validation using data from Shaanxi, Yangtze River Delta, and Pearl River Delta from 2015 to 2024 confirms model accuracy. For instance, in Shaanxi, node count grew from 50 to 900, average degree from 2.40 to 5.00, average shortest path length from 5.20 to 3.30, and integration degree from 0.20 to 0.68. Model error rates for key metrics are under 5% when compared to real data, as shown in Table 2. Shaanxi, as a resource-driven region, best fits Scheme 7 (error rates: average degree 1.0%, clustering coefficient 2.8%, integration degree 4.5%); Yangtze River Delta, a synergy-driven region, aligns with Scheme 11 (error rates: average degree 0.8%, path length 0.8%, integration degree 5.0%); Pearl River Delta, a market-driven region, matches Scheme 10 (error rates: average degree 0.5%, path length 2.1%, integration degree 2.3%).
| Region | Optimal Scheme | Average Degree Error Rate | Path Length Error Rate | Clustering Coefficient Error Rate | Integration Degree Error Rate |
|---|---|---|---|---|---|
| Shaanxi | 7 | 1.0% | 0.8% | 2.8% | 4.5% |
| Yangtze River Delta | 11 | 0.8% | 0.8% | 40.0% | 5.0% |
| Pearl River Delta | 10 | 0.5% | 2.1% | 28.0% | 2.3% |
In conclusion, this study develops a policy-driven evolutionary model for the dual-chain integration of electric cars, revealing dynamic patterns and synergistic mechanisms. The network exhibits scale-free properties, with policy coefficients $G$ and node capabilities $\alpha_i$, $\beta_i$ significantly driving network expansion, efficiency, and integration. The model’s low error rates validate its effectiveness for long-term simulation. Policy recommendations include establishing a dynamic monitoring platform for electric car dual-chain integration, implementing differentiated micro-policies based on node capabilities, and creating node elimination and replenishment mechanisms to foster innovation and industrial synergy. These insights provide a theoretical framework and practical strategies for enhancing the electric car industry’s resilience and growth.