Cluster oscillation and bifurcation of fractional-order Duffing system with two time scales

• 作者: Xianghong Li Yanli Wang Yongjun Shen
• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2020,（4）
• 所属期刊栏目: DYNAMICS,VIBRATION,AND CONTROL
• 页码范围: 926-932
• 页数: 7页
• 语种: 英文

摘要

The dynamical behavior on fractional-order Duffing system with two time scales is investigated,and the point-cycle coupling type cluster oscillation is firstly observed herein.When taking the fractional order as bifurcation parameter,the dynamics of the autonomous Duffing system will become more complex than the corresponding integer-order one,and some typical phenomenon exist only in the fractional-order one.Different attractors exist in various parameter space,and Hopf bifurcation only happens while fractional order is bigger than 1 under certain parameter condition.Moreover,the bifurcation behavior of the autonomous system may regulate dynamical phenomenon of the periodic excited system.It results into the point-cycle coupling type cluster oscillation when the fractional order is bigger than 1.The related generation mechanism based on slow-fast analysis method is that the slow variation of periodic excitation makes the system periodically visit different attractors and critical points of different bifurcations of the autonomous system.