Topological perturbations on resilience of the world trade competition network

Network resilience is the ability of a system to automatically adjust its activities to maintain essential functions when the external environment changes or when internal failures occur. In the context of trade networks, it encompasses the network's capacity to adapt, reorganize, and continue functioning effectively in the face of various challenges, such as geopolitical events, economic crises, or natural disasters. Network resilience in trade networks is crucial for ensuring the uninterrupted flow of goods, services, and capital across borders, which is essential for global economic stability and growth. A resilient trade network can absorb and mitigate the impact of disruptions, thereby reducing the risk of trade disruptions cascading into broader economic crises. Research on network resilience of high-dimensional complex network systems spans socio-economic systems, power networks, and ecosystems. Prior advances (e.g., Gao et al., 2016; Barzel et al., 2015) show that multidimensional systems can be characterized by control and state parameters and that microscopic dynamics can be inferred from responses to perturbations. Yet there is a lack of instrumental methods for assessing network resilience under multimodal perturbations in high-dimensional settings, highlighting the need to consider different topological perturbations and to develop dynamic models for evaluation. In socio-economic contexts, studies have explored resilience in payment networks, supply chains, urban economic networks, and production networks, often focusing on how structural features and competition affect stability. However, relatively few studies analyze the resilience of trade export networks, despite their central role in the socioeconomic system. Recent shocks such as COVID-19, tighter export controls, and shifting trade barriers underscore the importance of understanding how export competition intensity among countries impacts the stability of global trade. In this paper, we construct a World Trade Export Competition Network (WTCN) based on export similarity to capture competition intensity between countries and use a deformed Lotka-Volterra-based network dynamics model to evaluate resilience under eight types of topological perturbations (node, link, and weight). We aim to reveal how perturbations and competition intensity shape the resilience of the global export competition structure.

The paper surveys resilience research across complex systems, noting a shift from low-dimensional to high-dimensional models with identifiable state parameters (Gao et al., 2016) and methods to infer dynamics from perturbation responses (Barzel et al., 2015). Applications include urban traffic metastability (Zeng et al., 2020), city responses to external shocks (Ribeiro and Gonçalves, 2019), and power system vulnerability (Abedi et al., 2019; Das et al., 2020). In economic networks, studies have examined payment networks (de la Torre et al., 2016) and supply chain resilience from engineering and socio-ecological perspectives (Wieland and Durach, 2021). Urban economic and production networks have been analyzed to understand structural complexity and amplification of technological progress (Chen and Jiang, 2022; McNerney et al., 2022). Competition dynamics in socio-economic systems have been modeled with generalized Lotka-Volterra formulations (Saavedra et al., 2014). In trade, prior work on competition intensity often targeted specific commodities (e.g., coal, iron ore) rather than global export competition (Wang et al., 2021; Hao et al., 2018). Studies on PTAs and multiplex relations indicate complex effects on resilience (Mon et al., 2019; Liang, 2023). COVID-19’s impact on export disruption propagation has been assessed using network analysis (Brienen et al., 2023). This background motivates a comprehensive resilience analysis of a global export competition network, incorporating diverse topological perturbations.

World Trade Competition Network (WTCN): The WTCN G = (V, E) is an undirected weighted network where nodes are countries, links indicate export competition, and weights quantify competition intensity using the Export Similarity Index (ESI). ESI_ij = sum_k min(s_hat_ik, s_hat_jk), where s_hat_ik is the share of country i’s exports of product k in its total exports; ESI ranges in [0,1], with higher values indicating greater similarity and competition. Data: UN Comtrade Database, SITC Rev. 2 classification (786 products). A five-year window (2016–2020) is used, averaging to construct a representative network. For each country, the five partners with the highest competition intensity are retained to pre-process the network (robustness to keeping top 3 or top 10 partners is discussed in Supplementary Material S1). Network visualization shows node color darkness proportional to trade mean; the weight distribution PDF is provided. Resilience Dynamics Model: Starting from the general network dynamics dx_i/dt = F(x_i) + sum_j A_ij G(x_i, x_j), the study adopts a deformed general Lotka-Volterra model: F(x_i) = -x_i, G(x_i, x_j) = x_i x_j. Following Scheffer et al. (2001), two effective parameters link dynamics and structure, yielding a one-dimensional model: f(beta_eff, x_eff) = -x_eff + beta_eff * x_eff^2/(x_eff + 1). Here x_eff = <s>, the weighted average degree; beta_eff = (s_out s_in)^(1/2). This reduction permits simulation of topological perturbation impacts on resilience via the generic resilience function. Topological Perturbations: Eight perturbation types across nodes, links, and weights. Node removal strategies: (1) random removal; (2) removal by node degree order (largest-first and smallest-first); (3) removal by node weighted degree order (largest-first and smallest-first). Link removal strategies: (1) random removal; (2) removal by link weight order (highest-first and lowest-first). Weight change strategies: (1) Randomly retain a given proportion of weights (10%, 50%, 100%), set others to zero, randomly reshuffle weight positions, then progressively reduce weights in steps of 2%; (2) Retain top 20% highest-weight links or bottom 20% lowest-weight links, reshuffle weight positions, then progressively reduce weights to study sensitivity to competition intensity. Experimental Setup: Stochastic procedures (random node/link removal; weight-change experiments) are repeated 100 times to average out randomness; deterministic orders (degree-based node removal; weight-based link removal) are executed once. Node removal proceeds one node at a time to highlight contrasts given the modest network size. Before weight-change perturbations, weight positions are reshuffled 300 times. Resilience is tracked versus percentage reduction in nodes, links, or weights, decreasing weights by 2% per step.

- Node removal: Random removal causes a gradual decline in resilience. Degree-ordered removal shows faster resilience loss when removing high-degree nodes first, with a collapse observed when about 40% of nodes are removed. Weighted-degree-ordered removal similarly shows that removing higher weighted-degree nodes first decreases resilience more rapidly than removing lower weighted-degree nodes first. These results indicate that nodes with larger degree or higher weighted degree disproportionately support network resilience. - Link removal: Random link removal steadily reduces resilience. Removal prioritized by higher link weight (i.e., higher competition intensity) causes a faster decline in resilience than removing lower-weight links first, indicating that high-intensity competitive relationships are critical to stability. - Weight change (sparsity): With only 10% of weights retained, the maximum mean resilience is small and fluctuations are large; as weights are reduced further, resilience can increase transiently but the system is highly unstable and prone to collapse. With 50% of weights retained, the overall weight reduction of about 10% leads to an average resilience of zero, indicating a complete loss of resilience; the maximum resilience is higher than in the 10% case, suggesting that additional links can raise peak resilience even if the average collapses sooner. With 100% of weights retained (original network), maximum resilience is highest, and complete loss of resilience occurs only after approximately a 50% reduction in weights, showing that retaining more links slows resilience degradation due to weight reduction. - Weight change (competition intensity composition): Retaining the bottom 20% of low-weight links yields extremely small maximum resilience with large fluctuations, indicating instability. Retaining the top 20% of high-weight links produces a smoother decline and eventual loss of resilience as weights decrease, implying that higher competition intensity makes the network more stable. - Model fit: Empirical perturbation results (node, link, weight changes) map onto the same curve in (beta_eff, x_eff) space, aligning with the generic resilience function and exhibiting a first-order transition around B ≈ 2, demonstrating that the dynamical function captures the WTCN’s resilience behavior. Overall, the intensity of export competition strongly influences resilience: targeted removal of high-intensity nodes/links accelerates resilience loss, while maintaining a higher share of high-intensity competition links enhances stability.

The study addresses how export competition intensity and topological perturbations shape the resilience of the global export competition network. By constructing the WTCN via export similarity and applying a deformed Lotka-Volterra dynamics, the analysis demonstrates that structural features tied to competition intensity are pivotal for stability. High-degree and high weighted-degree countries serve as resilience anchors; their removal precipitates rapid resilience decline. Similarly, high-intensity competition links are crucial; their removal undermines stability faster than removing weaker links. Weight-change experiments reveal that networks preserving a larger fraction of high-intensity links sustain higher maximum resilience and exhibit more stable trajectories under weight reductions. Mapping perturbation outcomes into beta_eff–x_eff space shows that diverse micro-level perturbations collapse onto a universal resilience curve, supporting the generality of the dynamics-based resilience framework. These findings have real-world relevance: changes in participation or behavior of major trading countries (e.g., policy shifts or trade disputes such as the Sino–US trade war) can alter competition intensity and thus network stability. Policymakers aiming to preserve global trade stability should consider strategies that maintain or bolster robust, high-intensity competitive ties and avoid disproportionate disruption to highly connected or highly competitive nodes and links.

The paper constructs a World Trade Competition Network (WTCN) using export similarity (ESI) over 2016–2020 and evaluates resilience under eight topological perturbations via a deformed Lotka-Volterra dynamics model. Key contributions include: (1) a comprehensive, global export competition network capturing competition intensity; (2) systematic perturbation experiments across nodes, links, and weights; and (3) empirical validation that perturbation outcomes align with a generic resilience function in beta_eff–x_eff space. Results show that removing high-degree or high weighted-degree countries, or removing high-intensity competition links, accelerates resilience loss. Weight-change experiments indicate that networks with a higher proportion of high-intensity links are more stable and maintain higher maximum resilience, whereas sparsity and low-intensity compositions render the network unstable. These insights suggest that sustaining strong competitive interactions between countries helps preserve global trade network stability. Future research could incorporate multiple additional factors affecting resilience in complex trade networks, explore temporal dynamics beyond a five-year average, and consider multiplex relations (e.g., trade agreements, political ties) to enrich resilience assessments.

- Data coverage and construction: The WTCN uses UN Comtrade export data averaged over 2016–2020 and retains only the top five competition partners per country; while robustness to keeping top 3 or top 10 partners is discussed in supplementary material, this preprocessing and averaging may omit temporal variability and weaker competitive ties. - Scope of factors: The analysis focuses on topological perturbations (nodes, links, weights) and competition intensity derived from ESI; other factors influencing resilience (e.g., multiplex relations, policy regimes, supply chain dependencies) are not explicitly modeled, as noted by the authors as avenues for future work. - Network coverage: The world trade export data do not include every country globally, implying potential omissions that can affect observed resilience patterns. - Simulation design: Stochastic perturbations are averaged over 100 runs and weights are reduced in fixed 2% steps after reshuffling; different stochastic schemes or parameterizations might yield quantitative differences, though qualitative patterns are robust.