In this paper, we investigate the dynamics of the periodic motion for switched van der Pol equation with impulsive effect, utilizing the theory of mapping dynamics in switching systems. For the optimized problem, we consider such impulsive dynamical model as switched system and analyze its features from a discontinuous point of view. Then, conceptions of switching sets as well as discrete mappings are briefly reviewed. By constructing generic mappings, we analyze the flow's periodic behaviors from the perspective of mapping structures. Finally, we apply our analysis and criterion to a specific impulsive model at fixed points and the periodic motions with impulse to the boundary are illustrated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.