On two-parameter bifurcation analysis of the periodic parameter-switching Lorenz oscillator
On two-parameter bifurcation analysis of the periodic parameter-switching Lorenz oscillator
复制标题
DOI：
10.1007/s11071-015-2012-6
复制
发表时间：
2015-03
影响因子：
5.6
通讯作者：
Chun Zhang;Qinsheng Bi
中科院分区：
文献类型：
--
作者：
Chun Zhang;Qinsheng Bi
通过将周期性参数切换方案引入到洛伦兹振荡器中，建立了一个切换动力学模型。为了研究切换系统的行为机制，用合适的局部截面和局部映射定义了整个系统的庞加莱图。可以观察到系统中不同类型的周期振荡及其向混沌的转变。根据与周期解相关联的相应不动点的Floquet乘通过单位圆的条件，在分岔参数平面上得到了一些分岔曲线，将参数平面划分为几个区域，对应不同的振荡类型。同时，确定了切换系统的分叉场景，如折岔、干草叉和倍周期分叉。
By introducing the periodic parameter-switching scheme to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the switched system, the Poincaré map of the whole system is defined by suitable local sections and local maps. Different types of periodic oscillations and their transitions to chaos in the system can be observed. Based on the conditions when the Floquet multiplies of corresponding fixed point associated with the periodic solution pass the unit circle, some bifurcation curves are obtained in the plane of bifurcation parameters, dividing the parameters plane into several regions corresponding to different kinds of oscillations. Meanwhile, bifurcation scenarios, such as fold bifurcation, pitchfork bifurcation and period-doubling bifurcation, are determined in the switched system.