Self-excited and hidden attractors in a multistable jerk system

Abstract

In this paper we investigate a jerk system which is modeled by a homogeneous third-order ordinary differential equation, with four parameters that control the dynamics. The proper choice of one of these parameters allows the system to display real or non-real equilibrium points. This implies that we can choose such a parameter so that the associated attractors are either self-excited or hidden. We consider the two situations, and investigate the dynamics of the two versions of this jerk system, in cross-sections of the three-dimensional parameter-space generated by the other three parameters. We show that both versions of the jerk system display multistability, with coexistence of periodic–periodic, chaotic–chaotic, and periodic–chaotic attractors in the phase-space, regardless of whether the attractors are self-excited or hidden. We also show that basins of attraction and attractors occupy smaller volumes in the case of the system with no equilibrium points.