Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (5): 173-181.doi: 10.16088/j.issn.1001-6600.2020121402

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Research on Complex Dynamics of a New Four-dimensional Hyperchaotic System with Finite and Infinite Isolated Singularities

RUAN Wenjing, YANG Qigui*   

  1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China
  • Received:2020-12-14 Revised:2021-02-03 Online:2021-09-25 Published:2021-10-19

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Abstract: Based on the Sprott A chaotic system, by designing a feedback controller, this paper proposes a new four-dimensional autonomous hyperchaotic system with an infinite number of isolated singularities and only two symmetrical singularities. The stability of the non-hyperbolic singularities of this type of new system is discussed by using the central manifold theory, and the Hopf bifurcation is strictly proved. Furthermore, by using numerical methods such as Lyapunov exponential spectrum, bifurcation graph and Poincaré mapping, the existence of periodic attractors, chaotic attractors and hyperchaotic attractors of the new system is obtained.

Key words: hyperchaos, attractor, Hopf bifurcation, complex dynamics, stability

CLC Number: 

  • O415.5
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