A new fractional-order complex chaotic system with extreme multistability and its implementation

In this paper, a new fractional-order complex chaotic system (FOCCS) is proposed and studied. Firstly, the dissipativity and stability are discussed. Secondly, the dynamical characteristics of the system with parameters and order changes are analyzed by using phase diagrams, Lyapunov exponent (LEs) and bifurcation diagrams, respectively. In addition, the dynamical behavior is discussed for q of integer and fractional orders. In particular, the attractor coexistence is found, such as the coexistence of chaotic attractor and chaotic attractor, and chaotic attractor and periodic attractor. Interestingly, the multiple attractors coexistence is found by changing the initial conditions with fixed parameters. Finally, it is implemented on the analog circuit and DSP platform. The study provide a reference for the research and application of chaos.