Van der Pol oscillators generated from grazing dynamics

In this paper, we take into account two coupled Van der Pol equations with impacts. The main novelty is that the degenerated system for the model admits an oscillation with zero impact velocity. To prove presence of oscillations, beside the perturbation method, the newly developed linearization for dynamics with grazing has been applied. As different from the theoretical results such as Nordmark mapping and Zero time discontinuity mapping, the grazing is examined through another method of discontinuous dynamics, which diminishes the role of mappings in the analysis. The rich diversity of changes in the dynamics is observed under regular perturbations, since of the grazing discontinuity. By means of the simulation results, the analytical studies are visualized.