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Two pairs of heteroclinic orbits coined in a new sub-quadratic Lorenz-like system

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Abstract

This paper reports a new 3D sub-quadratic Lorenz-like system and proves the existence of two pairs of heteroclinic orbits to two pairs of nontrivial equilibria and the origin, which are completely different from the existing ones to the unstable origin and a pair of stable nontrivial equilibria in the published literature. This motivates one to further explore it and dig out its other hidden dynamics: Hopf bifurcation, invariant algebraic surface, ultimate boundedness, singularly degenerate heteroclinic cycle and so on. Particularly, numerical simulation illustrates that the Lorenz-like chaotic attractors coexist with one saddle in the origin and two stable nontrivial equilibria, which are created through the broken infinitely many singularly degenerate heteroclinic cycles and explosions of normally hyperbolic stable foci \(E_{z}.\)

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There is no data because the results obtained in this paper can be reproduced based on the information given in this paper.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 12001489, in part by Natural Science Foundation of Zhejiang Guangsha Vocational and Technical University of construction under Grant 2022KYQD-KGY, in part by Zhejiang Public Welfare Technology Application Research Project of China Grant LGN21F020003, in part by Natural Science Foundation of Taizhou University under Grant T20210906033, and in part by NSF of Zhejiang Province under Grant LY20A020001, LQ18A010001. At the same time, the authors wish to express their sincere thanks to the anonymous editors and reviewers for their conscientious reading and numerous valuable comments which improved immensely the presentation of this paper.

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Authors and Affiliations

  1. School of Electronic and Information Engineering (School of Big Data Science), Taizhou University, Taizhou, 318000, People’s Republic of China

    Haijun Wang & Qifang Su

  2. School of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang, 322100, Zhejiang, People’s Republic of China

    Guiyao Ke

  3. School of Information Engineering, GongQing Institute of Science and Technology, Gongqingcheng, 332020, People’s Republic of China

    Guiyao Ke

  4. Department of Big Data Science, School of Science, Zhejiang University of Science and Technology, Hangzhou, 310023, People’s Republic of China

    Jun Pan & Hongdan Fan

  5. College of Sustainability and Tourism Ritsumeikan Asia Pacific University, Jumonjibaru, Beppu, Oita, 874-8577, Japan

    Feiyu Hu

Authors
  1. Haijun Wang
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  2. Guiyao Ke
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  3. Jun Pan
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  5. Hongdan Fan
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Contributions

HW: conceptualization, software, writing—original draft, visualization, investigation. GK: supervision, software, methodology, investigation, visualization. JP: software, visualization, validation, writing—review and editing. FH: software, validation. HF: software, validation, writing—review and editing. QS: validation, writing—review and editing.

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Correspondence to Guiyao Ke.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Wang, H., Ke, G., Pan, J. et al. Two pairs of heteroclinic orbits coined in a new sub-quadratic Lorenz-like system. Eur. Phys. J. B 96, 28 (2023). https://doi.org/10.1140/epjb/s10051-023-00491-5

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