Period-additivity and multistability in piecewise smooth systems

Abstract

Piecewise smooth systems have been consistently considered and investigated in nonlinear dynamics due to their practical applications. In this paper, we study a generic type of piecewise smooth dynamical system to deal with period-additivity and multistability in the system; an arithmetic sequence of periodic attractors appearing in the period-adding bifurcation and the coexistence of multiple attractors in the system. We state a physical observation of the phenomena and then provide rigorous mathematical arguments and numerical simulations.