Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (5): 433-444.doi: 10.16088/j.issn.1001-6600.2020022803

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Complex Dynamics of a Six-dimensional Hyperchaotic System with Four Positive Lyapunov Exponents

SHAO Huiting, YANG Qigui*   

  1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China
  • Received:2022-02-28 Revised:2022-03-26 Online:2022-09-25 Published:2022-10-18

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Abstract: Based on the Lorenz system, a new six-dimensional hyperchaotic system with four positive Lyapunov exponents is found with only one hyperbolic equilibrium point by using coupling techniques and linear feedback control in this paper. Meanwhile, the system has three positive Lyapunov exponents for infinitely many equilibrium lines. The stability of the hyperbolic equilibrium point is analyzed by using Routh-Hurwitz criterion, and the existence of Hopf bifurcation is proved. Using computer simulation techniques such as phase diagram, Lyapunov exponential spectrum, Poincaré map, and bifurcation diagram, the complex dynamic evolution process of the six-dimensional hyperchaotic system from periodic, quasi-periodic, chaotic to hyperchaotic is analyzed numerically.

Key words: six-dimensional hyperchaotic system, attractor, Hopf bifurcation, complex dynamics, stability

CLC Number: 

  • O175
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