Dynamics, Periodic Orbit Analysis, and Circuit Implementation of a New Chaotic System with Hidden Attractor

Hidden attractors are associated with multistability phenomena, which have considerable application prospects in engineering. By modifying a simple three-dimensional continuous quadratic dynamical system, this paper reports a new autonomous chaotic system with two stable node-foci that can generate...

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Bibliographic Details
Published in:Fractal and fractional 2022-04, Vol.6 (4), p.190
Main Author: Dong, Chengwei
Format: Article
Language:English
Subjects:
Analog circuits
Attractors (mathematics)
Basins
Chaos theory
Circuits
Coordinate transformations
Dynamical systems
Eigenvalues
electronic circuit
Electronic circuits
Equilibrium
hidden attractor
Initial conditions
Liapunov exponents
Orbital mechanics
Orbits
Parameters
Realizability
symbolic dynamics
unstable periodic orbit
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Summary:Hidden attractors are associated with multistability phenomena, which have considerable application prospects in engineering. By modifying a simple three-dimensional continuous quadratic dynamical system, this paper reports a new autonomous chaotic system with two stable node-foci that can generate double-wing hidden chaotic attractors. We discuss the rich dynamics of the proposed system, which have some interesting characteristics for different parameters and initial conditions, through the use of dynamic analysis tools such as the phase portrait, Lyapunov exponent spectrum, and bifurcation diagram. The topological classification of the periodic orbits of the system is investigated by a recently devised variational method. Symbolic dynamics of four and six letters are successfully established under two sets of system parameters, including hidden and self-excited chaotic attractors. The system is implemented by a corresponding analog electronic circuit to verify its realizability.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6040190