Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks
Year: 2022
Author: Mi Zhou, Zhengdong Du
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 1 : pp. 18–41
Abstract
In this paper, we study heteroclinic bifurcation and the appearance of chaos in time-perturbed piecewise smooth hybrid systems with discontinuities on finitely many switching manifolds. The unperturbed system has a heteroclinic orbit connecting hyperbolic saddles of the unperturbed system that crosses every switching manifold transversally, possibly multiple times. By applying a functional analytical method, we obtain a set of Melnikov functions whose zeros correspond to the occurrence of chaos of the system. As an application, we present an example of quasi-periodically excited piecewise smooth system with impacts formed by two linked rocking blocks.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2022.18
Journal of Nonlinear Modeling and Analysis, Vol. 4 (2022), Iss. 1 : pp. 18–41
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Melnikov method Hybrid system Heteroclinic bifurcation Chaos Linked rocking blocks.
Author Details
Mi Zhou Email
Zhengdong Du Email