Abstract
This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.
Highlights
Entropy 2021, 23, 1341. https://Since the first chaotic system with a hidden attractor in Chua’s system was discovered [1], hidden attractors have motivated great interest because of their importance in both theory and engineering
If the basin of attraction is associated with an unstable equilibrium, it is a self-excited attractor, if the basin of attraction does not intersect with small neighbourhoods of any equilibrium, it is the hidden attractor [4,5]
The dynamical properties of the chaotic system have been analyzed by several numerical methods
Summary
Since the first chaotic system with a hidden attractor in Chua’s system was discovered [1], hidden attractors have motivated great interest because of their importance in both theory and engineering. There are two kinds of attractors classified by Kuznetsov et al [2]: self-excited attractor [3] and hidden attractor. If the basin of attraction is associated with an unstable equilibrium, it is a self-excited attractor, if the basin of attraction does not intersect with small neighbourhoods of any equilibrium, it is the hidden attractor [4,5]. Multi-stability is an important phenomenon, meaning an infinite number of attractors generated through varying the initial values or system parameters. Pham et al investigated the multi-stability of a novel hidden chaotic system without equilibrium [13] Yang et al
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