Modelling and dynamic analysis of a novel seven-dimensional Hamilton conservative hyperchaotic systems with wide range of parameter

Abstract

The study of chaotic attractors has been a hot issue in complex science research in recent years. However, most of the current research has focused on low-dimensional dissipative systems. High-dimensional conservative systems have both conservative and hyperchaotic properties, the phase space is integer dimensional and does not have attractors, and the trajectories expand in multiple directions, thus having higher complexity and spatial ergodicity. In addition, the high dimensional conservative system with wide parameter range not only has better dynamic characteristics, but also has a good application prospect in the field of information security. In this paper, a novel seven-dimensional Hamiltonian conservative hyperchaotic system (7D-HCHCS) is constructed. The dynamical properties of this system are described by analyzing the rate of change of phase space volume, phase trajectory diagram, Poincaré map, Lyapunov exponential spectrum (LEs), bifurcation diagram, equilibrium point, and system complexity. A new pseudo-random number generator (PRNG) is designed on this basis, and the key stream generated by this PRNG passes the NIST test. Besides, the phase diagrams and Poincaré map under a wide range of parameters are compared. The results show that the proposed system satisfies the Hamilton energy conservation and can generate hyperchaotic flow. It also has good pseudorandom characteristics, ergodicity under a large range of control parameters, which also has good prospects in the field of information security.