Periodic Motion of the van der Pol Equation with Impulsive Effect

Abstract

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.

Analysis of Discontinuous Dynamical Behaviors of a Friction-Induced Oscillator with an Elliptic Control Law

“…In the next year, Luo and Rapp [2] studied the motions and switchability of an oscillator in a periodically forced, discontinuous system with switching control law of a parabolic boundary. In 2015, Zheng and Fu [53] proposed the switched Van der Pol equation with impulsive effect as switched system and analyzed its features from a discontinuous point of view. In 2017, Fan et al [54] studied discontinuous dynamics of a friction-induced oscillator with switching control law of a straight line.…”