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 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 quasiperiodically excited piecewise smooth system with impacts formed by two linked rocking blocks.