Numerical Analysis of a Novel 3D Chaotic System with Period-Subtracting Structures

Abstract

In this work, we present a novel three-dimensional chaotic system with only two cubic nonlinear terms. Dynamical behavior of the system reveals a period-subtracting bifurcation structure containing all [Formula: see text]th-order ([Formula: see text]) periods that are found in the dynamical evolution of the novel system concerning different values of parameters. The new system could be evolved into different states such as point attractor, limit cycle, strange attractor and butterfly strange attractor by changing the parameters. Also, the system is multistable, which implies another feature of a chaotic system known as the coexistence of numerous spiral attractors with one limit cycle under different initial values. Furthermore, bifurcation analysis reveals interesting phenomena such as period-doubling route to chaos, antimonotonicity, periodic solutions, and quasi-periodic motion. In the meantime, the existence of periodic solutions is confirmed via constructed Poincaré return maps. In addition, by studying the influence of system parameters on complexity, it is confirmed that the chaotic system has high spectral entropy. Numerical analysis indicates that the system has a wide variety of strong dynamics. Finally, a message coding application of the proposed system is developed based on periodic solutions, which indicates the importance of studying periodic solutions in dynamical systems.

A Hidden Chaotic System with Multiple Attractors

“…Recently, the SE algorithm has been used to analyze the dynamic characteristics of chaotic systems. Zolfaghari-Nejad et al confirmed the period-subtracting phenomenon through SE distribution diagram [31]. Wang et al analyzed the basic dynamics of a fractional-order chaotic system with a hidden system by comparing LLE and SE algorithms in [32], and the SE algorithm was also used to exhibit multi-stability under different initial values [33][34][35].…”