A new class of Hamiltonian conservative chaotic systems with multistability and design of pseudo-random number generator

Abstract

• A new modeling method is employed to develop a class of high dimensional Hamiltonian conservative chaotic systems. • A new conservative hyperchaotic system is proposed and exhibits some behaviour previously unobserved. • Multistability including infinite-orbit and infinite-scroll is observed in the proposed systems. • For encryption, pseudo-random digital signal generators based on conservative chaotic systems are developed. Compared to dissipative chaotic system, conservative chaotic systems have some attractive features valuable for engineering applications, such as security communication. This paper proposes a method for constructing new high dimensional conservative chaotic systems, for instance 4 dimensional conservative chaotic systems and 5 dimensional conservative hyper-chaotic systems. The dynamic properties of the constructed systems are verified by the dynamical evolution map, equilibrium points, Lyapunov dimension, the volume of flow and the Hamiltonian energy. An interesting co-existence of quasi-period, chaos and hyper-chaos flows are observed in the developed conservative chaotic systems. With trigonometric transformation, parallel conservative chaotic systems are achieved with infinitely many scrolls. To accommodate the engineering application requirement, the security communication is considered as a case study. The proposed conservative chaotic systems passed the validation National Institute of Standard Statistic Test criteria for the pseudo-random property , which is the critical factor of security communication. Furthermore, the pseudo-random signal generator is developed using the Field Programmable Gate Array technique. Due to the complicated topology structure, such digital implementation was not commonly reported in literatures, instead most conservative chaotic systems were validated only by analog circuit simulation.