Dynamics study, synchronous control and encryption applications of chaotic systems with extreme multi-stability and multi-vortices

In this paper, we propose a four-dimensional chaotic system with infinite unstable equilibrium points, extreme homogeneous multi-stability as well as extreme heterogeneous multi-stability, and the change from single vortex to multi-vortices can be achieved by varying the chaotic system parameters and initial conditions. The rich dynamics of the new chaotic system are demonstrated through the analysis of phase diagrams, Lyapunov exponents, etc. We have experimentally confirmed its offset-enhancing property. The feasibility of this chaotic system model is verified through electronic circuit simulation using Multisim software. In addition, in order to achieve the control of the proposed chaotic system, a complete synchronization controller is systematically designed and implemented, demonstrating successful synchronization of two chaotic systems with matching topological structures. It is worth noting that this complete synchronization controller can regulate the synchronization establishment time by changing its built-in parameters, More importantly, the message encryption applications not only conclusively verify the synchronization controller’s effectiveness but also demonstrate the proposed chaotic system’s engineering applicability.