Study of mixed-mode oscillations in a parametrically excited van der Pol system
Study of mixed-mode oscillations in a parametrically excited van der Pol system
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DOI：
10.1007/s11071-014-1377-2
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发表时间：
2014-04
影响因子：
5.6
通讯作者：
Xiujing Han;Qinsheng Bi;Chun Zhang;Yue Yu
中科院分区：
文献类型：
--
作者：
Xiujing Han;Qinsheng Bi;Chun Zhang;Yue Yu
研究了慢变参数激励对货车der Pol系统动力学的影响。当参数激励缓慢通过受控货车der Pol系统的Hopf分岔值时，系统表现出周期分岔延迟行为。第一个分支延迟行为依赖于初始条件，而跟随第一个分支延迟行为是免疫初始条件。这些分叉延迟行为导致尖峰吸引子和静止状态之间的滞后环，这是负责混合模式振荡的产生。然后，基于分岔延迟行为，提出了一种近似计算混合模式振荡中每簇重复尖峰脉冲中尖峰脉冲个数的方法。理论结果与数值模拟结果吻合较好。
This paper investigates the effects of slowly varying parametric excitation on the dynamics of van der Pol system. Periodic bifurcation delay behaviors are exhibited when the parametric excitation slowly passes through Hopf bifurcation value of the controlled van der Pol system. The first bifurcation delay behavior relies on initial conditions, while the bifurcation delay behaviors that follow the first one are immune to initial conditions. These bifurcation delay behaviors result in a hysteresis loop between the spiking attractor and the rest state, which is responsible for the generation of mixed-mode oscillations. Then an approximate calculation for the number of spikes in each cluster of repetitive spiking of mixed-mode oscillations is explored based on bifurcation delay behaviors. Theoretical results agree well with numerical simulations.