| Zhouchao Wei |
| School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China |
Abstract: The Melnikov method is extended to a class of hybrid piecewise-smooth systems with impulsive effect and noise excitation when the unperturbed system is a piecewise Hamiltonian system with a homoclinic orbit. The homoclinic orbit continuously crosses the first switching manifold and transversally jumps across the second switching manifold by impulsive effect. The trajectory of the corresponding perturbed system crosses the first switching manifold by applying the reset map describing the impact rule instantaneously. Then, the random Melnikov process of such systems is derived and the criteria for the onset of chaos with or without noise excitation are established. In addition, the complicated dynamics of a concrete piecewise-smooth system with or without noise excitation under the reset maps, impulsive effect, non-autonomous periodic and damping perturbations are investigated by this extended method and numerical simulations.