A class of higher-dimensional hyperchaotic maps

Abstract

Based on the hybrid modulation coupling (HMC) pattern, a class of higher-dimensional (HD) hyperchaotic maps is proposed using three one-dimensional (1D) seed maps. The seed maps are chaotic maps or the combination of chaotic maps and non-chaotic maps. Taking the HMC of iterative chaotic map with infinite collapse (ICMIC), Sine map and a linear map (ISL-HMC) as an example, the equilibrium points are mathematically analyzed. The dynamical performance of the 3D ISL-HMC map is evaluated by phase diagram, Lyapunov exponents (LEs), bifurcation diagram and chaos diagram. Furthermore, compared with existing chaotic maps, complexity and distribution characteristic are analyzed. As application of the ISL-HMC map, a pseudorandom number generator (PRNG) is designed and tested by NIST SP 800-22 and TestU01. Experimental results show that the ISL-HMC map has rich dynamical behaviors and good randomness. So this class of HD hyperchaotic maps is a potential model for cryptography and other applications.