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

In this paper, we study heteroclinic bifurcation and the appearance of chaos in time-perturbed piecewise smooth hybrid systems with discontinuitieson finitely many switching manifolds. The unperturbed system has a heteroclinic orbit connecting hyperbolic saddles of the unperturbed systemthat crosses every switching manifold transversally, possibly multiple times. By applying a functional analytical method, we obtain a set of Melnikovfunctions whose zeros correspond to the occurrence of chaos of the system. As an application, we present an example ofquasiperiodically excited piecewise smooth system with impacts formed by two linked rocking blocks.