Bursting oscillations with a codimension-2 non-smooth bifurcation in a piecewise-smooth system of Filippov type

Wang, Zhixiang; Zhang, Chun; Bi, Qinsheng

doi:10.1016/j.chaos.2024.115040

Chaos, Solitons & Fractals

2024

DOI: 10.1016/j.chaos.2024.115040

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Bursting oscillations with a codimension-2 non-smooth bifurcation in a piecewise-smooth system of Filippov type

Zhixiang Wang,

Chun Zhang,

Qinsheng Bi

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2024

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Dynamical analysis of bursting in a system with a discontinuous boundary involving two state variables

Zuo,

Zhu,

Song

et al. 2024

Phys. Scr.

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This paper investigates the bursting oscillations and the underlying dynamical mechanisms of a non-smooth system with a discontinuous boundary that involves two state variables. A slow-fast non-smooth system is established after modifying the Chua's circuit. By applying the variable substitution, the system with a boundary involving two state variables is transformed into a system where the boundary involves only a single state variable. The topological equivalence between the systems before and after the transformation is demonstrated. The stability analysis is performed on the transformed system, and the bifurcation conditions are given. Six types of bursting oscillation patterns under different parameter settings are presented. The bifurcation transition mechanisms of these bursting patterns are revealed using two-dimensional transformed phase diagrams. It is found that an increase in the excitation amplitude leads to changes in the transition patterns of the system trajectory between point and cycle, resulting in the formation of a 'sticking' special spiking state. This spiking state involves multiple limit cycle attractors and an equilibrium branch. The magnitude of the excitation amplitude also affects the slow passage effect of the system, determining whether the trajectory undergoes periodic oscillations at the Hopf bifurcation point.

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Dynamical analysis of bursting in a system with a discontinuous boundary involving two state variables

Zuo,

Zhu,

Song

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

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Bursting oscillations with a codimension-2 non-smooth bifurcation in a piecewise-smooth system of Filippov type

Cited by 1 publication

References 23 publications

Dynamical analysis of bursting in a system with a discontinuous boundary involving two state variables

Dynamical analysis of bursting in a system with a discontinuous boundary involving two state variables

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