A new 4D hyperchaotic system and its control

Ning Cui; Junhong Li; Ning Cui; Junhong Li

doi:10.3934/math.2023044

AIMS Mathematics

2023, Volume 8, Issue 1: 905-923. doi: 10.3934/math.2023044

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Research article Special Issues

A new 4D hyperchaotic system and its control

Ning Cui ,
Junhong Li ^,

School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, China

Received: 28 July 2022 Revised: 21 September 2022 Accepted: 28 September 2022 Published: 13 October 2022
MSC : 34K18, 65P20

This paper presents a new four-dimensional (4D) hyperchaotic system by introducing a linear controller to 3D chaotic Qi system. Based on theoretical analysis and numerical simulations, the dynamical behaviors of the new system are studied including dissipativity and invariance, equilibria and their stability, quasi-periodic orbits, chaotic and hyperchaotic attractors. In addition, the Hopf bifurcation at the zero equilibrium point and hyperchaos control of the system are investigated. The numerical simulations, including phase diagram, Lyapunov exponent spectrum, bifurcations and Poincaré maps are carried out in order to analyze and verify the complex phenomena of the 4D hyperchaotic system.
- hyperchaos,
- Lyapunov exponents,
- bifurcation,
- hyperchaos control
Citation: Ning Cui, Junhong Li. A new 4D hyperchaotic system and its control[J]. AIMS Mathematics, 2023, 8(1): 905-923. doi: 10.3934/math.2023044

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Abstract

This paper presents a new four-dimensional (4D) hyperchaotic system by introducing a linear controller to 3D chaotic Qi system. Based on theoretical analysis and numerical simulations, the dynamical behaviors of the new system are studied including dissipativity and invariance, equilibria and their stability, quasi-periodic orbits, chaotic and hyperchaotic attractors. In addition, the Hopf bifurcation at the zero equilibrium point and hyperchaos control of the system are investigated. The numerical simulations, including phase diagram, Lyapunov exponent spectrum, bifurcations and Poincaré maps are carried out in order to analyze and verify the complex phenomena of the 4D hyperchaotic system.

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