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摘要: 为探索无穷多共存吸引子是否存在公共的Wada域边界这一问题，推广了Nusse-Yorke的有限Wada域定理到无穷多Wada域的情况。基于数值实验，我们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的复杂的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。
基金资助:山东省自然科学基金（ZR2021MA095）; 国家自然科学基金重点项目资助（11732014）![]()
Complex
Wada Basin Analysis of Infinite Coexisting Attractors in a Class of OscillatorsSchool of Mathematics and
Statistics, Qingdao UniversityAbstract: 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.Keywords: wada basin; basin of attraction; coexisting
attractors; megastability王敬伟（1998-），男，山东青岛人，硕士研究生，主要研究方向为非线性动力学，复杂系统等。王敬伟.一类振荡器的无穷多共存吸引子复杂Wada域分析[DB/OL].(2023-09-13).http://kns.cnki.net/kcms/detail/37.1402.N.20230912.1234.002.html.![]()
