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.
Highlights
As a typical non-smooth dynamic system, the Filippov system reflected in the mathematical model can be expressed as discontinuous differential equations whose right-hand side is discontinuous [1]
Based on the results of the analysis of the equilibria and the tangential singularities of Equation (6), we find that mixed-mode oscillations are obtained when the whole system undergoes a transformation between the fast system and slow system connected by the different types of tangential points on the switched surface
We study the evolution of the mixed-mode oscillation dynamics and the associated mechanism of the non-smooth behaviors at the switching boundary when the amplitude A is changed
Summary
As a typical non-smooth dynamic system, the Filippov system reflected in the mathematical model can be expressed as discontinuous differential equations whose right-hand side is discontinuous [1]. Many important practical engineering problems involve coupling of different time scales [13,14,15,16] This type of system may cause mixed-mode oscillations, which are formed by a relatively large excursion and nearly harmonic small amplitude oscillation during every evolution period. This paper investigates the mixed-mode oscillations and non-smooth dynamical behaviors in a piecewise nonlinear system with external excitation, focusing on the effects of the tangential singularities on the mixed-mode oscillations. For this purpose, we continue to analyze a realistic model in the literature [30], focusing on the effect of the external excitation.
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