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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.

Research on discrete memristor models applied to discrete maps deserves more in-depth discussion. In this paper, a continuous memristor is introduced and the discrete memristor model is obtained by the forward Eulerian difference algorithmic discretization. This model is coupled to a cosine map to further obtain a two-dimensional memristor cosine map. The dynamical characteristics of the memristor cosine map are investigated through numerical simulations and other analytical methods. For example, the phase diagram, the bifurcation diagram, the Lyapunov exponential spectrum and the Spectral Entropy complexity with parameters, etc., In addition, multi-stability phenomena of the system are identified. The results show that the cosine map coupled with a discrete memristor has more complex dynamical behaviors and is more suitable for applications in cryptography.