Dynamical behavior and control of a new hyperchaotic Hamiltonian system

Junhong Li; Ning Cui; Junhong Li; Ning Cui

doi:10.3934/math.2022285

AIMS Mathematics

2022, Volume 7, Issue 4: 5117-5132. doi: 10.3934/math.2022285

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Research article

Dynamical behavior and control of a new hyperchaotic Hamiltonian system

Junhong Li ,
Ning Cui ^,

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

Received: 13 September 2021 Revised: 15 December 2021 Accepted: 23 December 2021 Published: 31 December 2021
MSC : 34K18, 34H10, 65P20

In this paper, we firstly formulate a new hyperchaotic Hamiltonian system and demonstrate the existence of multi-equilibrium points in the system. The characteristics of equilibrium points, Lyapunov exponents and Poincaré sections are studied. Secondly, we investigate the complex dynamical behaviors of the system under holonomic constraint and nonholonomic constraint, respectively. The results show that the hyperchaotic system can generated by introducing constraint. Additionally, the hyperchaos control of the system is achieved by applying linear feedback control. The numerical simulations are carried out in order to analyze the complex phenomena of the systems.
- Hamiltonian system,
- hyperchaos,
- constraint,
- hyperchaos control
Citation: Junhong Li, Ning Cui. Dynamical behavior and control of a new hyperchaotic Hamiltonian system[J]. AIMS Mathematics, 2022, 7(4): 5117-5132. doi: 10.3934/math.2022285

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Abstract

In this paper, we firstly formulate a new hyperchaotic Hamiltonian system and demonstrate the existence of multi-equilibrium points in the system. The characteristics of equilibrium points, Lyapunov exponents and Poincaré sections are studied. Secondly, we investigate the complex dynamical behaviors of the system under holonomic constraint and nonholonomic constraint, respectively. The results show that the hyperchaotic system can generated by introducing constraint. Additionally, the hyperchaos control of the system is achieved by applying linear feedback control. The numerical simulations are carried out in order to analyze the complex phenomena of the systems.

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