Dynamics of a New Multi-Cavity Hyperchaotic Map and Its DSP Implementation

Abstract

A new higher-dimensional hyperchaotic map, named Sine Chebyshev modulation map (SCMM), is proposed based on the closed-loop modulation coupling (CMC) model. The dynamics of the SCMM are evaluated by attractor diagrams, Lyapunov exponents and bifurcations. By designing a piecewise-linear function, the SCMM is expanded to the grid multi-cavity form. Dynamical behaviors of the two-dimensional grid multi-cavity SCMM are then analyzed. The results show that it has rich dynamical characteristics, including complicated phase space trajectories, hyperchaotic behaviors, large maximum Lyapunov exponent and typical bifurcations. The complexity of the new grid multi-cavity hyperchaotic map is large in the entire parameter space. Finally, digital circuits of 2D-SCMM and 2D grid multi-cavity SCMM are implemented based on the DSP technique. The feasibility of the circuit is verified, and it lays the foundation for applications in chaotic secure communication.