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Volume 4, Issue 1
Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks

Mi Zhou & Zhengdong Du

DOI: 10.12150/jnma.2022.18

J. Nonl. Mod. Anal., 4 (2022), pp. 18-41.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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  • 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.

  • Keywords

Melnikov method, Hybrid system, Heteroclinic bifurcation, Chaos, Linked rocking blocks.

  • AMS Subject Headings

34C23, 34C37, 37C29

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-18, author = {Zhou , Mi and Du , Zhengdong}, title = {Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {1}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.18}, url = {http://global-sci.org/intro/article_detail/jnma/20691.html} }
TY - JOUR T1 - Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks AU - Zhou , Mi AU - Du , Zhengdong JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 18 EP - 41 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.18 UR - https://global-sci.org/intro/article_detail/jnma/20691.html KW - Melnikov method, Hybrid system, Heteroclinic bifurcation, Chaos, Linked rocking blocks. AB -

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.

Zhou , Mi and Du , Zhengdong. (2022). Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks. Journal of Nonlinear Modeling and Analysis. 4 (1). 18-41. doi:10.12150/jnma.2022.18
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