Multitudinous potential homoclinic and heteroclinic orbits seized

Haijun Wang; Jun Pan; Guiyao Ke; Haijun Wang; Jun Pan; Guiyao Ke

doi:10.3934/era.2024049

Electronic Research Archive

2024, Volume 32, Issue 2: 1003-1016. doi: 10.3934/era.2024049

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Research article

Multitudinous potential homoclinic and heteroclinic orbits seized

Haijun Wang ¹,
Jun Pan ^{2
,
,},
Guiyao Ke ^{3,4,5
,
,}

1.
School of Electronic and Information Engineering (School of Big Data Science), Taizhou University, Taizhou, 318000, China
2.
Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
3.
School of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang, Zhejiang 322100, China
4.
HUIKE Education Technology Group Co., Ltd., China
5.
School of Information Engineering, GongQing Institute of Science and Technology, Gongqingcheng 332020, China

Received: 04 October 2023 Revised: 10 November 2023 Accepted: 16 November 2023 Published: 19 January 2024

Revisiting a newly reported modified Chen system by both the definitions of $ \alpha $-limit and $ \omega $-limit set, Lyapunov function and Hamiltonian function, this paper seized a multitude of pairs of potential heteroclinic orbits to (1) $ E_{0} $ and $ E_{\pm} $, or (2) $ E_{+} $ or (3) $ E_{-} $, and homoclinic and heteroclinic orbits on its invariant algebraic surface $ Q = z - \frac{x^{2}}{2a} = 0 $ with cofactor $ -2a $, which is not available in the existing literature to the best of our knowledge. Particularly, the theoretical conclusions were verified via numerical examples.
- new 3D modified Chen system,
- multi-wing chaotic attractor,
- homoclinic and heteroclinic orbit,
- Lyapunov function
Citation: Haijun Wang, Jun Pan, Guiyao Ke. Multitudinous potential homoclinic and heteroclinic orbits seized[J]. Electronic Research Archive, 2024, 32(2): 1003-1016. doi: 10.3934/era.2024049

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Abstract

Revisiting a newly reported modified Chen system by both the definitions of $ \alpha $-limit and $ \omega $-limit set, Lyapunov function and Hamiltonian function, this paper seized a multitude of pairs of potential heteroclinic orbits to (1) $ E_{0} $ and $ E_{\pm} $, or (2) $ E_{+} $ or (3) $ E_{-} $, and homoclinic and heteroclinic orbits on its invariant algebraic surface $ Q = z - \frac{x^{2}}{2a} = 0 $ with cofactor $ -2a $, which is not available in the existing literature to the best of our knowledge. Particularly, the theoretical conclusions were verified via numerical examples.

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