摘要
针对一类周期激励下的广义离散Duffing系统,运用快慢分析方法,对系统状态进行数值模拟,通过分岔图和时间历程图对系统进行分析,得到不同参数下系统所表现出的新型簇发振荡模式,并探讨其与连续Duffing系统之间的联系.系统的簇发振荡模式被分为两类,一类是当慢变量穿过Fold分岔点或混沌激变点,吸引子发生转迁所诱发的各种对称式簇发振荡,另一类则是当慢变量无法穿过Fold分岔点或混沌激变点,由延迟Flip分岔所诱发的各种非对称式簇发振荡.
For a class of generalized discrete Duffing systems with periodic excitations,a fast-slow analysis method is applied to simulate the system by time course diagrams and bifurcation diagrams to obtain new types of cluster oscillations under different parameters and to explore the connection between them and continuous Duffing systems.The cluster oscillation modes are divided into two categories,one is the symmetric cluster oscillation induced by the attractor transitions when the slow variable crosses the Fold bifurcation point or the chaotic excitation point,and the other is the asymmetric cluster oscillation induced by the delayed Flip bifurcation when the slow variable cannot cross the Fold bifurcation point or the chaotic excitation point.
作者
冷萌萌
钱有华
Leng Mengmeng;Qian Youhua(School of Mathematical Sciences,Zhejiang Normal University,Jinhua 321004,China)
出处
《动力学与控制学报》
2023年第10期18-25,共8页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(12172333)
关键词
广义离散Duffing系统
簇发振荡
混沌激变
快慢分析法
分岔分析
generalized discrete duffing systems
cluster-emitting oscillations
chaotic excitations
fast and slow analysis method
bifurcation analysis
