Nonlinear Behavior of a Novel Switching Jerk System

Abstract

This paper proposes a novel chaotic jerk system, which is defined on four domains, separated by codimension-2 discontinuity surfaces. The dynamics of the proposed system are conveniently described and analyzed through a generalization of the Poincaré map which is constructed via an explicit solution of each subsystem. This provides an approach to formulate a robust bifurcation problem as a nonlinear inhomogeneous eigenvalue problem. Also, we establish some criteria for the existence of a period-doubling bifurcation and discuss some of the interesting categories of complex behavior such as multiple period-doubling bifurcations and chaotic behavior when the trajectory undergoes a segment of sliding motion. Our results emphasize that the sharp switches in the behavior are mainly responsible for generating new and unique qualitative behavior of a simple linear system as compared to the nonlinear continuous system.