A new hyperchaotic particle motion system and its control

Ning Cui and Junhong Li
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Ning Cui: School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, P. R. China
Junhong Li: School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, P. R. China†School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 12, 1-18

Abstract: This paper formulates a new hyperchaotic system for particle motion. The continuous dependence on initial conditions of the system’s solution and the equilibrium stability, bifurcation, energy function of the system are analyzed. The hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane are also investigated. It shows that the rich dynamic behaviors of the system, including the degenerate Hopf bifurcations and nondegenerate Hopf bifurcations at multiple equilibrium points, the irregular variation of Hamiltonian energy, and the hyperchaotic attractors. These results generalize and improve some known results about the particle motion system. Furthermore, the constraint of hyperchaos control is obtained by applying Lagrange’s method and the constraint change the system from a hyperchaotic state to asymptotically state. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich hyperchaotic behaviors.

Keywords: Particle motion; bifurcation; Hamiltonian energy; hyperchaos; hyperchaos control (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0129183120500047

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