Routes to bursting oscillations in a modified van der Pol-Duffing oscillator with slow-varying periodic excitation
Routes to bursting oscillations in a modified van der Pol-Duffing oscillator with slow-varying periodic excitation
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具有慢变周期性激励的改进型 van der Pol™ Duffing 振荡器中爆发振荡的路线
DOI：
10.1177/1077546317740020
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发表时间：
2018-11-01
影响因子：
2.8
通讯作者：
Guo Hulun
中科院分区：
文献类型：
--
作者：
Ma Xindong;Cao Shuqian;Guo Hulun
本文研究了具有慢变周期激励的修正van der Pol-Duffing电路系统的动力学行为和机制。通过对平衡状态的分析，发现当参数缓慢变化时，系统的稳定平衡和极限环振荡会发生切换。当参数在不同的参数范围内缓慢变化时，可以观察到周期振荡和猝发振荡，尤其是一种由Hopf分叉时滞引起的猝发振荡。详细研究了这些由Hopf-分叉-延迟引起的突发模式，从而产生了复合分类，即“延迟supHopf/Fold Cycle-subHopf/supHopf”突发和通过“延迟supHopf/supHopf”滞后环的“subHopf/supHopf”突发。
The present study examines the dynamical behaviors and the mechanism of a modified van der Pol-Duffing circuit system with slow-varying periodic excitation. Based on the analysis of the equilibrium states, the stable equilibrium and limit cycle oscillation are found to switch as the parameter slowly varies. The periodic and bursting oscillations are observed as the parameter slowly varies within the different parameter regions, especially one type of Hopf-bifurcation-delay-induced bursting oscillation. These Hopf-bifurcation-delay-induced bursting patterns are studied in detail, thereby generating compound classifications, namely "delayed supHopf/fold cycle-subHopf/supHopf" bursting and "subHopf/supHopf" bursting via "delayed supHopf/ supHopf" hysteresis loop.