Dynamics of a hyperchaotic map with spherical attractor

Abstract

This paper presents a novel three-dimensional hyperchaotic map with the spherical attractor. The typical dynamic properties of the new chaotic system are evaluated by attractor diagrams, Lyapunov exponent (LE), bifurcations and permutation entropy (PE) complexity. The results show that it has rich dynamical behaviors, including hyperchaos, large Lyapunov exponent and typical bifurcations. There are also some unusual features, such as coexisting attractors and plane equilibrium. To improve its performance, we extend the attractor space by adding the staircase wave function to the new system. Compared with the original system, the expanded system has a larger complexity and more complex topology. By controlling the system parameters, it can effectively improve the PE complexity of the system. Finally, the digital circuit of the new system is realized based on DSP technology, and the feasibility of the system model is verified. The proposed hyperchaotic map has advantages in complexity and rich dynamic characteristics, which has good application prospects in secure communication.