网络拓扑对混沌系统同步能力的影响
The Influence of Network Topology on the Synchronization Capability of Chaotic Systems
摘要: 本文探讨了不同网络中耦合的Rössler振子的同步能力问题。首先，我们使用数值方法对单个Rössler系统进行求解，观察到混沌现象的发生。接着，基于主稳定函数法，通过求解最大Lyapunov指数，得到系统理论上发生同步的临界耦合强度。同时，利用同步误差函数，得到了数值上的临界耦合强度。通过对比这两种方法得到的结果，评估混沌系统的同步能力，并推测了网络拓扑的平均度与网络同步能力之间存在密切关系。
Abstract: This paper explores the synchronization capability of coupled Rössler oscillators in different networks. Firstly, we employ numerical methods to solve for a single Rössler system, observing the occurrence of chaotic phenomena. Next, based on the method of Master Stability Function, we determine the critical coupling strength for synchronization theoretically by solving for the maximum Lyapunov exponent. Simultaneously, utilizing the synchronization error function, we obtain the critical coupling strength numerically. By comparing the results obtained from these two methods, we assess the synchronization capability of chaotic systems and speculate on the close relationship between the average degree of network topology and network synchronization capability.
文章引用：张彦超, 王鑫乐, 赵安旭, 赵楠楠. 网络拓扑对混沌系统同步能力的影响[J]. 应用数学进展, 2024, 13(6): 2761-2770. https://doi.org/10.12677/aam.2024.136265

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