广义Chua电路簇发现象及其分岔机理

Bursting phenomenon and the bifurcation mechanism in generalized Chua's circuit

通过引入由电感和电阻组成的控制电路模块,并适当选定参数,建立了具有快慢效应的四阶广义Chua电路的模型.探讨了快子系统随慢变量变化产生fold分岔及Hopf分岔的条件,进而探讨了整个系统的动力学演化过程,重点分析了系统中存在的各种快慢效应,给出了两种典型的对称式fold/fold和fold/Hopf周期簇发现象及其相应的分岔机制,从分岔的角度,指出了两种簇发现象的本质区别.

By introducing the electrical controlling circuit composed of inductance and capacitance,a fourth order model of generalized Chua＇s circuit with fast-slow effect has been established for certain parameter conditions.The conditions for fold bifurcation as well as Hopf bifurcation of the fast subsystem are investigated with the variation of the slow variable.Furthermore,the dynamical evolution of the entire system is explored,in which the fast-slow effect existing in the system is focused.Two types of bursting phenomenon,namely,the symmetric fold/fold and fold/Hopf periodic bursters,as well as their mechanism,are presented,which discloses the difference between the two burstings from the view point of bifurcation.