Hidden Extreme Multistability in a Novel No-Equilibrium Fractional-Order Chaotic System and Its Synchronization Control

Chaotic systems with hidden attractors have received widespread attention recently. In this paper, we construct a new four-dimensional fractional-order chaotic system by adding a further variable in a 3D chaotic system. This newly presented system has no equilibrium points, which reveals that the attractors produced by this system are all hidden. The intricate hidden dynamic properties are investigated by adopting nonlinear dynamical analysis tools such as phase diagrams, bifurcation diagrams, Lyapunov exponents, and chaos diagrams. In particular, the coexisting hidden attractors and extreme multistability are also observed in the system. Furthermore, the electronic circuit of this chaotic system is designed and the corresponding hardware circuit experiment is also achieved. Finally, based on the theory of fractional finite time stability theorem, a suitable finite time synchronization controller is designed. Numerical simulations are provided to verify the effectiveness of the proposed synchronization scheme.