一类振荡器的无穷多共存吸引子复杂Wada域分析  

Complex Wada Basin Analysis of Infinite Coexisting Attractors in a Class of Oscillators

作　　者：王敬伟 WANG Jingwei(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071

出　　处：《复杂系统与复杂性科学》2024年第4期48-52,共5页Complex Systems and Complexity Science

基　　金：山东省自然科学基金(ZR2021MA095);国家自然科学基金重点项目(11732014)。

摘　　要：为探索无穷多共存吸引子是否存在公共Wada域边界的问题,推广Nusse-Yorke的有限Wada域定理到无穷多Wada域。基于数值实验,在一类非线性振荡器发现了无穷多共存吸引子具有公共的吸引域边界,且这些吸引子在空间分布上呈现周期性。进一步分析了吸引子复杂的Wada吸引域结构,通过推广的Nusse-Yorke关于Wada域的判定定理,证实了这些连通的Wada域具有公共边界。最后指出这种类型的Wada域边界表现出了非常复杂的非线性动力学特性,可能导致高度的不确定性以及对初始条件的极端敏感依赖性。To explore the question of whether there exist common Wada basin boundaries among an infinite number of coexisting attractors,we extended Nusse-Yorke′s theorem for finite Wada basins to the scenario of infinite Wada basins.Through numerical experiments conducted on a class of nonlinear oscillators,we discovered that within this class,there are infinite coexisting attractors that share common basin boundaries,and these attractors exhibit periodic spatial distributions.Further analysis of the intricate Wada basin structures associated with these attractors,employing a generalized version of Nusse-Yorke′s theorem concerning Wada basins,confirmed the presence of common boundaries among these interconnected Wada basins.Finally,it is essential to note that this type of Wada basin boundary exhibits highly complex nonlinear dynamical characteristics,potentially leading to significant uncertainty and extreme sensitivity to initial conditions.

关 键 词：Wada域 吸引域 共存吸引子 超稳态 

分 类 号：N93[自然科学总论] O193[理学—数学]