Design and Dynamics of Multicavity Hyperchaotic Maps with Cylinder Attractors

Abstract

Based on the mathematical model of the elliptical cylinder, we design a new hyperchaotic map with an elliptical cylinder or a cylinder attractor. The dynamical analysis results indicate the proposed system is globally hyperchaotic, and has large Lyapunov Exponents (LEs), and high Permutation Entropy (PE) complexity. Interestingly, the hyperchaotic system exhibits the offset boosting coexistence attractors with respect to the system parameters. In addition, three Multicavity Hyperchaotic Maps (MHCM) are constructed by introducing a symmetric staircase function, which expands greatly the phase space of the system. The MHCM have more complex topological structures and maintain the chaotic performance of the original map. To illustrate the feasibility of the hyperchaotic systems further, we apply them to design a Pseudo-Random Number Generator (PRNG), and implement them on the DSP platform.