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 - <p style="text-align: justify;">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.</p>