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Multitudinous potential hidden Lorenz-like attractors coined

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Abstract

Very little research is available in the field of sub-quadratic chaotic systems. This note reports a new 3D sub-quadratic Lorenz-like system: \({\dot{x}}=a(y - x)\), \({\dot{y}}=c\root 3 \of {x} - \root 3 \of {x}z\), \({\dot{z}}= -bz + \root 3 \of {x}y\). Except for the rich dynamics, i.e., generic and degenerate pitchfork bifurcation, first integral, invariant algebraic surface, ultimate bounded set, singularly degenerate heteroclinic cycle with nearby chaotic attractor, and existence of a pair of heteroclinic orbits, etc., this proposed system gives birth to Lorenz-like chaotic attractors coexisting the unstable origin and two stable node-foci in a broad range of the parameter c and thus hidden attractors are coined, which verifies the guess that the decrease of powers of some variable states may widen the ranges of some parameters for which hidden attractors exist. This may not only provide a new method to detect hidden Lorenz-like attractors, but also pose an interesting problem that the existence of hidden attractors can be determined by the degrees of the variables of the studied systems.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical study or no experimental data has been listed.]

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Acknowledgements

This work is supported in part National Natural Science Foundation of China under Grant 12001489, in part Zhejiang Public Welfare Technology Application Research Project of China(Grant: LGN21F020003), in part Natural Science Foundation of Taizhou University (Grant: T20210906033), in part NSF of Zhejiang Province under Grant LY20A020001, LQ18A010001, in part NSF of Zhejiang University of Science and Technology under Grant F702108J03 and Grant F701108G13. 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 extremely improve the presentation of the 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

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

    Guiyao Ke

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

    Jun Pan & Feiyu Hu

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

    Hongdan Fan

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  1. Haijun Wang
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Correspondence to Guiyao Ke.

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CRediT authorship contribution statement

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

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Wang, H., Ke, G., Pan, J. et al. Multitudinous potential hidden Lorenz-like attractors coined. Eur. Phys. J. Spec. Top. 231, 359–368 (2022). https://doi.org/10.1140/epjs/s11734-021-00423-3

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