Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks (Journal of Nonlinear Modeling and Analysis, 2024)
In this paper, we study heteroclinic bifurcation and the appearanceof chaos in time-perturbed piecewise smooth hybrid systems with discontinuities on finitely many switching manifolds. The unperturbed system has aheteroclinic 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 Melnikov functions whose zeros correspond to the occurrence of chaos of the system. Asan application, we present an example of quasi-periodically excited piecewisesmooth system with impacts formed by two linked rocking blocks.
Keywords: Melnikov method; Hybrid system; Heteroclinic bifurcation; Chaos; Linked rocking blocks.