Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System

Chun Zhang and Qiaoxia Tang
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Chun Zhang: School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China
Qiaoxia Tang: School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China

Mathematics, 2022, vol. 10, issue 5, 1-11

Abstract: The main task of this article is to study the patterns of mixed-mode oscillations and non-smooth behaviors in a Filippov system with external excitation. Different types of periodic spiral crossing mixed-mode oscillation patterns, i.e., “cusp-F − /fold-F − ” oscillation, “cusp-F − /two-fold/two-fold/fold-F − ” oscillation and “two-fold/fold-F − ” oscillation, are explored. Based on the analysis of the equilibrium and tangential singularities of the fast subsystem, spiral crossing oscillation around the tangential singularities is investigated. Meanwhile, by combining the fast and slow analysis methods, we can observe that the cusp, two-fold and fold-cusp singularities play an important role in generating all kinds of complex mixed-mode oscillations.

Keywords: mixed-mode oscillations; tangential singularity; spiral crossing oscillations; external excitation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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