Dynamics, control and symmetry breaking aspects of an infinite-equilibrium chaotic system

Abstract

It is well known that the symmetry break deliberately induced in a nonlinear system may help to discover new nonlinear patterns. In this work, we investigate the impact of an explicit symmetry break on the dynamics of a recently introduced chaotic system with a curve of equilibriums (Pham et al. in Circuits Syst Signal Process 37(3):1028–1043, 2018). We demonstrate that the symmetry break engenders rich and striking nonlinear phenomena including the coexistence of multiple asymmetric stable states, the presence of parallel bifurcation branches, hysteresis, and critical transitions as well. A simple control strategy based on linear augmentation technique that enables to drive the system from the state of four coexisting self-excited attractors to a monostable state is successfully adapted. To the best of the authors’ knowledge, this work represents the first report on symmetry breaking for a chaotic system with infinite equilibriums and thus deserves dissemination.