Delayed SubHopf-Fold/Fold Cycle簇发振荡及其动力学转迁  

Delayed SubHopf-Fold/Fold Cycle Bursting Oscillation as Well as its Dynamical Transitions

作　　者：张真真 ZHANG Zhenzhen(Jiangsu University JingJiang College,212013,Zhenjiang,Jiangsu,PRC)

机构地区：[1]江苏大学京江学院,江苏镇江212013

出　　处：《江西科学》2020年第4期460-465,606,共7页Jiangxi Science

摘　　要：基于周期激励下的van der Pol-Duffing振子,研究了一类由Hopf分岔滞后引起的delayed subHopf-fold/fold cycle簇发振荡及其动力学转迁,这种簇发模式表现出余维-2簇发振荡特性。将周期激励看做慢变量,得到了快子系统和慢子系统。然后对快子系统进行分岔分析,给出了Hopf分岔和fold分岔的临界条件。最后利用分岔图和转换相图的叠加分析了该簇发振荡的产生机制及其动力学转迁。Based on the van der Pol-Duffing oscillator with a slow-varying periodic excitation,a novel bursting pattern named delayed subHopf-fold/fold cycle bursting oscillation and its transitions are revealed.The characteristics of codimension-2 bifurcation can be found in this bursting.The fast subsystem and the slow subsystem can be obtained by regarding the excitation as a slow-changing variable.Then,the critical conditions of Hopf bifurcation and fold bifurcation are given through the bifurcation analysis of the fast subsystem.Finally,the mechanism as well as the dynamical transitions of this bursting are analyzed by superimposing the transition phase diagram onto the bifurcation diagram.

关 键 词：分岔滞后 余维-2分岔 簇发振荡 van der Pol-Duffing方程 

分 类 号：O31[理学—一般力学与力学基础]