A hyperchaos generated from Rabinovich system

Junhong Li; Ning Cui; Junhong Li; Ning Cui

doi:10.3934/math.2023071

AIMS Mathematics

2023, Volume 8, Issue 1: 1410-1426. doi: 10.3934/math.2023071

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Research article

A hyperchaos generated from Rabinovich system

Junhong Li ,
Ning Cui ^,

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

Received: 08 July 2022 Revised: 29 September 2022 Accepted: 13 October 2022 Published: 20 October 2022
MSC : 34K18, 65P20

In this paper, we present a 4D hyperchaotic Rabinovich system which obtained by adding a linear controller to 3D Rabinovich system. Based on theoretical analysis and numerical simulations, the rich dynamical phenomena such as boundedness, dissipativity and invariance, equilibria and their stability, chaos and hyperchaos are studied. In addition, the Hopf bifurcation at the zero equilibrium point of the 4D Rabinovich system is investigated. The numerical simulations, including phase diagrams, Lyapunov exponent spectrum, bifurcations, power spectrum and Poincaré maps, are carried out in order to analyze and verify the complex phenomena of the 4D Rabinovich system.
- Rabinovich system,
- hyperchaos,
- Lyapunov exponents,
- bifurcation
Citation: Junhong Li, Ning Cui. A hyperchaos generated from Rabinovich system[J]. AIMS Mathematics, 2023, 8(1): 1410-1426. doi: 10.3934/math.2023071

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Abstract

In this paper, we present a 4D hyperchaotic Rabinovich system which obtained by adding a linear controller to 3D Rabinovich system. Based on theoretical analysis and numerical simulations, the rich dynamical phenomena such as boundedness, dissipativity and invariance, equilibria and their stability, chaos and hyperchaos are studied. In addition, the Hopf bifurcation at the zero equilibrium point of the 4D Rabinovich system is investigated. The numerical simulations, including phase diagrams, Lyapunov exponent spectrum, bifurcations, power spectrum and Poincaré maps, are carried out in order to analyze and verify the complex phenomena of the 4D Rabinovich system.

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