COMPLEX DYNAMICS OF A SIMPLE 3D AUTONOMOUS CHAOTIC SYSTEM WITH FOUR-WING

Xianyi Li; Chang Li; Haijun Wang

doi:10.11948/2017047

2017 Volume 7 Issue 2

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Xianyi Li, Chang Li, Haijun Wang. COMPLEX DYNAMICS OF A SIMPLE 3D AUTONOMOUS CHAOTIC SYSTEM WITH FOUR-WING[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 745-769. doi: 10.11948/2017047

Citation:

Xianyi Li, Chang Li, Haijun Wang. COMPLEX DYNAMICS OF A SIMPLE 3D AUTONOMOUS CHAOTIC SYSTEM WITH FOUR-WING[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 745-769. doi: 10.11948/2017047

COMPLEX DYNAMICS OF A SIMPLE 3D AUTONOMOUS CHAOTIC SYSTEM WITH FOUR-WING

1 Department of Mathematics and Information Science, Zhejiang University of Science and Technology, 310023 Hangzhou, China;
2 Department of Mathematics, South China Normal University, 510631 Guangzhou, China

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Abstract

Abstract

The present paper revisits a three dimensional (3D) autonomous chaotic system with four-wing occurring in the known literature[Nonlinear Dyn (2010) 60(3):443-457] with the entitle "A new type of four-wing chaotic attractors in 3-D quadratic autonomous systems" and is devoted to discussing its complex dynamical behaviors, mainly for its non-isolated equilibria, Hopf bifurcation, heteroclinic orbit and singularly degenerate heteroclinic cycles, etc. Firstly, the detailed distribution of its equilibrium points is formulated. Secondly, the local behaviors of its equilibria, especially the Hopf bifurcation, are studied. Thirdly, its such singular orbits as the heteroclinic orbits and singularly degenerate heteroclinic cycles are exploited. In particular, numerical simulations demonstrate that this system not only has four heteroclinic orbits to the origin and other four symmetry equilibria, but also two different kinds of infinitely many singularly degenerate heteroclinic cycles with the corresponding two-wing and four-wing chaotic attractors nearby.
- Four-wing chaotic system /
- Hopf bifurcation /
- heteroclinic orbit /
- singularly degenerate heteroclinic cycle
MSC: 34C45;34C37;34D20

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References

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