A Torus-Chaotic System and Its Pseudorandom Properties

Abstract

Exploring and investigating new chaotic systems is a popular topic in nonlinear science. Although numerous chaotic systems have been introduced in the literature, few of them focus on torus-chaotic system. The aim of our short work is to widen the current knowledge of torus chaos. In this paper, a new torus-chaotic system is proposed, which has one positive Lyapunov exponent, two zero Lyapunov exponents, and two negative Lyapunov exponents. The dynamic behavior is investigated by Lyapunov exponents, bifurcations, and stability. The analysis shows that this system has an interesting route leading to chaos. Furthermore, the pseudorandom properties of output sequence are well studied and a random number generator algorithm is proposed, which has the potential of being used in several cyber security systems such as the verification code, secure QR code, and some secure communication protocols.