Numerical studies on a piecewise smooth vibro-impact system in parameters-state spaces

The present paper is devoted to the synthesis of Poincare mapping and global dynamics of a class of piecewise smooth vibro-impact systems with preloading. The periodic motions are identified numerically in bi-parameter planes. The transition law and the motion pattern are presented as island-like periodic windows. The coexistence of attractors and their basins of attraction in the state planes is then given by cell-to-cell mappings. The numerical results indicate that new attractors can be induced by boundary crises and grazing bifurcations. In the final analysis, the coexisting attractors in disparate regions of bi-parameter planes are subjected to numerical simulation in the joint parameter-state space. It offers a novel approach to the study of the global dynamics of piecewise smooth systems.