扩散耦合非线性系统的集群同步：基于收缩理论的方法
Cluster synchronization of diffusively-coupled nonlinear systems: A contraction based approach
AI总结：
本文基于收缩理论，提出新的集群同步条件，考虑网络结构和节点非线性动态差异，改进了非线性系统同步分析的条件。
摘要：
寻找促进网络振荡系统同步的条件对于理解广泛生物和机械系统至关重要。然而，文献中用于非线性系统线性耦合的同步条件通常不够严格，无法准确确定系统行为。本文利用收缩理论，推导出新的集群同步充分条件，基于网络结构，适用于每个节点内在非线性动态可能不同的网络。我们的结果要求网络连接满足集群输入等价条件，并探讨了该要求对网络动态的影响。对于应用于神经元脉冲动态网络，我们展示了新条件比之前使用非光滑李雅普诺夫函数的分析结果更严格。改进基于网络配置的集群同步发生分析条件是促进复杂振荡系统理解和控制的重要一步。
英文摘要：
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with neuronal spiking dynamics, we show that our new sufficient condition is tighter than those found in previous analyses which used nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex oscillatory systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
