融合适应度特性与可控耦合机制的相互依存网络系统中的意见动力学研究

Research on Opinion Dynamics in Interdependent Network Systems Incorporating Fitness Characteristics and Controllable Coupling Mechanisms

摘要: 文章深入研究了在相互依存网络中引入可控耦合机制以及融合节点适应度特性对意见动态特性的影响。通过概率互联和通信控制耦合强度，实现了对网络间交互程度的精准调节。系统中的每个代理不仅具有二元意见状态(+或−)，还包含适应度参数k，该参数随时间演化，其分布与代理的意见状态耦合，使得系统动态地发展出异质性和类似记忆的行为特征。通过调整概率h，即控制高适应度节点采取特定意见的倾向性，文章研究了在不同h条件下，系统收敛时间τ与系统规模N之间的关系。结果表明，τ~N，即二者呈线性关系。此外，耦合强度的变化会引发收敛时间的突变，反映出系统对该参数的高度敏感性。强耦合会加剧k值分布的极化性，导致分布呈现明显的群集态和辐射态。这种现象增强了相互依存网络间的同步性和一致性。然而，当初始意见分布满足d > 0.5(即+状态占比大于50%)时，耦合强度的增加会加剧网络间的纠缠程度，从而显著减缓系统的收敛过程。这些研究结果揭示了耦合机制与节点适应度在塑造复杂相互依存网络意见形成动态过程中的关键作用。

Abstract: This paper conducted an in-depth study of opinion dynamics on interdependent networks by introducing a controllable coupling mechanism and integrating node fitness characteristics into the system. The coupling strength is regulated through probabilistic interconnections and communication channels, enabling precise control over the degree of interaction between networks. Each agent in the system is characterized not only by a binary opinion state (+ or −) but also by a fitness parameter k, which evolves over time. The distribution of k is dynamically coupled with the opinions of the agents, allowing the system to naturally develop heterogeneity and memory-like behavior. By adjusting the probability h, which governs the tendency of high-fitness nodes to adopt specific opinions, this paper examined the relationship between the system’s convergence time (τ) and its size (N) under varying coupling strengths. Our findings reveal that τ~N, indicating a linear relationship. Moreover, changes in coupling strength can induce abrupt transitions in convergence time, reflecting a highly sensitive dependence on this parameter. Strong coupling amplifies the polarization of the k-value distribution, leading to the emergence of distinct clustered and radial states. This phenomenon enhances synchronization and consensus across interdependent networks. However, when the initial distribution of + and − states satisfies d > 0.5, an increase in coupling strength exacerbates the entanglement between networks, thereby significantly slowing down the convergence process. These results provide critical insights into the role of coupling mechanisms and node fitness in shaping the dynamics of opinion formation in complex interdependent systems.