Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks

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.