Extreme multistability of different order chaotic systems: discrete and continuous

Abstract

In this paper, we propose a scheme for designing extreme multistable synchronized systems by coupling two distinct chaotic systems of different dimensions. Such coupling configurations exhibit synchronized chaos in the system. In other words, the synchronized state is sensitively dependent on the initial conditions. This kind of synchronization is an example of extreme multistable synchronization. To achieve an extreme multistable system we introduce a new conjecture by choosing the controllers in such a way that all state variables maintain the constant difference. Furthermore, we demonstrate the applicability of our scheme in coupled chaotic systems modeled as 3D and 4D chaotic systems respectively. Finally, we show that extreme multistable synchronization can be achieved in coupled 1D Ricker maps. Simulation results are provided to validate the efficiency and effectiveness of our proposed scheme.