Chatter dynamic analysis for Van der Pol Equation with impulsive effect via the theory of flow switchability

• We present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems.
• To investigate the chatter dynamics on such system, we apply the theory of flow switchability in discontinuous dynamical systems.
• Some sufficient conditions for the absence of pulse phenomena are obtained by using mapping structures.

In this paper, the phenomenon of free vibrations in LC circuit was introduced as well as some restrictions in the application of triode. Then we optimize the problems and present a certain kind of Van der Pol Equations which can be considered as a class of second-order impulsive switched systems. To investigate the chatter dynamics on such system, we turn to look for conditions that keep the complex pulse phenomena absent. We introduce several conceptions of theory of flow switchability and analyze the flow’s dynamical behaviors such as transversal property at a boundary in the normal direction of separation surface by constructing generic mappings. Some sufficient conditions for the absence of pulse phenomena and numerical illustrations of periodic motions are obtained.