Relaxation oscillations induced by an order gap between exciting frequency and natural frequency
Relaxation oscillations induced by an order gap between exciting frequency and natural frequency
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DOI：
10.1007/s11431-015-0839-2
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Xiaoke Chen;Shaolong Li;Zhengdi Zhang;Qinsheng Bi
中科院分区：
文献类型：
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作者：
Xiaoke Chen;Shaolong Li;Zhengdi Zhang;Qinsheng Bi
本文的主要目的是显示的弛豫振荡，被称为爆裂现象，与周期性激励的耦合振子的激励频率和自然频率之间的顺序差距。当激振频率远小于固有频率时，可以观察到折叠/折叠、Hopf/Hopf等不同类型的猝发振荡。通过将整个激励项看作一个慢变参数，基于激励项在一个小得多的时间尺度上变化的事实，导出了广义自治系统的分岔集，它将参数空间划分为与不同类型的动力学行为相关联的若干区域.以两个具有典型分岔模式的情形为例，探讨了系统动力学随外激励幅值变化的演化规律。通过引入与广义自治系统分岔图重叠的变换相图，可以得到在静止态（QS）和重复尖峰态（SP）之间交替出现的突发振荡.研究发现，不仅量子点和随机点的形式，而且量子点和随机点之间的过渡点处的分支，都可能影响到猝发吸引子的结构。此外，与SP相关的振幅和频率可能取决于来自静态的分叉模式。
The main purpose of the paper is to display the relaxation oscillations, known as the bursting phenomena, for the coupled oscillators with periodic excitation with an order gap between the exciting frequency and the natural frequency. For the case when the exciting frequency is much smaller than the natural frequency, different types of bursting oscillations such as fold/fold, Hopf/Hopf bursting oscillations can be observed. By regarding the whole exciting term as a slow-varying parameter on the fact that the exciting term changes on a much smaller time scale, bifurcations sets of the generalized autonomous system is derived, which divide the parameter space into several regions associated with different types of dynamical behaviors. Two cases with typical bifurcation patterns are focused on as examples to explore the dynamical evolution with the variation of the amplitude of the external excitation. Bursting oscillations which alternate between quiescent states (QSs) and repetitive spiking states (SPs) can be obtained, the mechanism of which is presented by introducing the transformed phase portraits overlapping with the bifurcation diagrams of the generalized autonomous system. It is found that not only the forms of QSs and SPs, but also the bifurcations at the transition points between QSs and SPs, may influence the structures of bursting attractors. Furthermore, the amplitudes and the frequencies related to SPs may depend on the bifurcation patterns from the quiescent sates.