Connecting Curves as a Tool to Localize Hidden Attractors in a New Chaotic Hyperjerk System with No Equilibria

Abstract

Localizing hidden attractors of chaotic systems is practically and theoretically important. Differing from self-excited attractors, hidden ones do not have any equilibria on the boundaries of their basin of attraction. This characteristic makes hidden attractors hard to localize. Some theoretical and numerical methods have been developed to recognize these attractors, yet the problem remains highly uncertain. For this purpose, the theory of connecting curves is utilized in this work. These curves are one-dimensional set-points that describe the structure of chaotic attractors even in the absence of zero-dimensional fixed-points. In this study, a new four-dimensional chaotic system with hidden attractors is presented. Despite the controversial idea of connecting curves that pass through fixed-points, the connecting curves of a system with no equilibria are considered. This analysis confirms that connecting curves provide more critical information about attractors even if they are hidden.

A new chaotic jerk system with hidden heart-shaped attractor: dynamical analysis, multistability, connecting curves and its application in image encryption

“…However, the attractor spirals around this curve. Also, varying this parameter does not significantly change the connecting curve [59]. ) for red and blue attractors, respectively.…”