一类变形蔡氏电路在双频激励下的非线性动力学研究
Study on Nonlinear Dynamics of a Class of Deformed Chua’s Circuit under Dual-Frequency Excitation
DOI: 10.12677/AAM.2021.102068, PDF,   
作者: 李 亮：浙江师范大学，数学与计算机科学学院，浙江 金华
关键词: 蔡氏电路；混沌；折叠分岔；簇发振荡；Chua’s Circuit； Chaos； Folding Bifurcation； Cluster Oscillation
摘要: 本文考虑了一类典型的具有分段非线性电阻和双频激励的蔡氏电路，研究了分段光滑动力系统中的混沌、分岔行为。若改变系统的激励参数，可产生不同的分岔和混沌现象。通过慢变周期的激励项作为分岔参数，探讨了快速子系统的分岔行为，同时讨论了系统在两个激励频率相同和不同且成整数比时的簇发现象，通过理论方法和数值模拟分析了折叠分岔和Hopf分岔及混沌下的非线性动力学行为。
Abstract: This paper considers a typical Chua’s circuit with piecewise nonlinear resistance and dual-frequency excitation, and studies the chaos and bifurcation behavior in piecewise smooth dynamic system. If the excitation parameters of the system are changed, different bifurcation and chaos phenomena can be produced. The bifurcation behavior of the fast subsystem is discussed by taking the excitation term with slowly varying period as bifurcation parameter, and the bursting phenomenon of the system are discussed when the two excitation frequencies are the same or different and are in integral ratio. The nonlinear dynamic behaviors of folding bifurcation, Hopf bifurcation and chaos are analyzed by theoretical method and numerical simulation.
文章引用：李亮. 一类变形蔡氏电路在双频激励下的非线性动力学研究[J]. 应用数学进展, 2021, 10(2): 632-639. https://doi.org/10.12677/AAM.2021.102068

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