Design and dynamic analysis of a class of new 3-D discrete memristive hyperchaotic maps with multi-type hidden attractors

As a basic component with special nonlinearity, memristor is widely used in chaotic circuits. In this paper, based on the mathematical model of a discrete cosine memristor, we constructed a class of new 3-D discrete memristive chaotic maps (3DDMCM) with infinite equilibrium points or no equilibrium points. Theoretical analysis and numerical simulations demonstrate that the 3DDMCM can generate an arbitrary number of multi-type hidden attractors, including multi-wave, multi-cavity, multi-firework, and multi-diamond hidden attractors. The discovery of the novel dynamic property enriches the diversity of memristive chaotic maps. The control parameter μ can adjust the number of basic forms of various chaotic attractors, thereby producing phenomena similar to multi-scroll patterns. Specifically, when the number of basic forms is determined, the chaotic attractor undergoes further mutations by changing the control parameter b. The corresponding dynamic analysis indicates that the system possesses two positive Lyapunov exponents, high complexity, offset boosting, and various geometric control behaviors. Finally, a pseudo-random number generator (PRNG) with desirable statistical properties is constructed to lay the foundation for engineering applications in the field of chaotic secure communication. Additionally, we utilized a DSP development board to implement the 3DDMCM, thereby confirming the feasibility of this system.