On occurrence of mixed-torus bursting oscillations induced by non-smoothness
On occurrence of mixed-torus bursting oscillations induced by non-smoothness
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DOI：
10.1007/s11071-022-07504-5
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发表时间：
2022-05
影响因子：
5.6
通讯作者：
Qinsheng Bi;Shaomin Chen
中科院分区：
文献类型：
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作者：
Qinsheng Bi;Shaomin Chen
研究了两尺度耦合的高维非光滑系统的慢-快行为。提出了一些新的猝发吸引子和有趣的现象，特别是所谓的混合环面猝发振荡，即轨道沿沿着不同的环面依次运动，但猝发吸引子仍表现为准周期形式.基于一个四维双涡卷超混沌模型，建立了一个改进的非光滑慢-快模型。通过对光滑和非光滑分岔的分析，得到了随慢变参数变化的共存吸引子。随着激励振幅的增大，爆发振荡由周期吸引子转变为准周期吸引子，其机理是利用变换后的相图与共存吸引子的重叠以及分岔现象得到的。在爆发吸引子上可以观察到沿轨道边界的沿着滑动，其机制可以用非光滑理论或两个伪吸引子在不同区域的相互影响来解释.由不稳定焦点定义的超锥可能导致尖峰振荡的周期增加或周期减少现象，而折叠极限环分叉可能导致尖峰振幅的剧烈变化。不同的极限环可能涉及全矢量场，导致所谓的混合环面爆发振荡，其中静态似乎是振荡的支点。
The paper devotes to the slow–fast behaviors of a higher-dimensional non-smooth system with the coupling of two scales. Some novel bursting attractors and interesting phenomena are presented, especially the so-called mixed-torus bursting oscillations, in which the trajectory moves along different tori in turn, though the bursting attractor still behaves in quasi-periodic form. Based on a 4-D hyper-chaotic model with two scrolls, a modified non-smooth slow–fast version is established. Upon the smooth and non-smooth bifurcations analysis, the coexisted attractors with the variation of the slow-varying parameter are derived. With the increase in the exciting amplitude, bursting oscillations may change from periodic to quasi-periodic attractor, the mechanism of which is obtained by employing the overlap of the transformed phase portrait and coexisted attractors as well as the bifurcations. Sliding along the boundary on the trajectory can be observed on the bursting attractor, the mechanism of which can be accounted for by employing the non-smooth theory or by the in-turn influence of two pseudo-attractors in different regions. Super-cone defined by an unstable focus may lead to the period-adding or period-decreasing phenomena in the spiking oscillations, while fold limit cycle bifurcation may result in the dramatical change of the spiking amplitude. Different limit cycles may involve the full vector field, resulting in the so-called mixed-torus bursting oscillations, in which the quiescent states seem to be pivots of the oscillations.