Grazing and Symmetry-Breaking Bifurcations Induced Oscillations in a Switched System Composed of Duffing and van der Pol Oscillators

Chun Zhang, Qiaoxia Tang and Zhixiang Wang
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Chun Zhang: School of Mathematical Science, Huaiyin Normal University, Huai’an 223300, China
Qiaoxia Tang: School of Mathematical Science, Huaiyin Normal University, Huai’an 223300, China
Zhixiang Wang: School of Mathematical Science, Huaiyin Normal University, Huai’an 223300, China

Mathematics, 2022, vol. 10, issue 5, 1-10

Abstract: By introducing a switching scheme related to the state and time, a typical switched model alternating between a Duffing oscillator and van der Pol oscillator is established to explore the typical dynamical behaviors as well as the mechanism of the switched system. Shooting methods to locate the limit cycle and specify bifurcation sets are described by defining an appropriate Poincaré map. Different types of multiple-Focus/Cycle and single-Focus/Cycle period oscillations in the system can be observed. Symmetry-breaking, period-doubling, and grazing bifurcation curves are obtained in the plane of bifurcation parameters, dividing the parameters plane into several regions corresponding to different kinds of oscillations. Meanwhile, based on the numerical simulation and bifurcation analysis, the mechanisms of several typical dynamical behaviors observed in different regions are presented.

Keywords: switched system; mixed-mode oscillation; nonsmooth evolution; bifurcation mechanism; transformed phase portrait (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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