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Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed

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  • Guiyao Ke

    (School of Information, Zhejiang Guangsha Vocational and Technical University of Construction, Dongyang 322100, China
    School of Information Engineering, GongQing Institute of Science and Technology, Gongqingcheng 332020, China
    HUIKE Education Technology Group Co., Ltd., Beijing 100191, China)

Abstract

Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of mathematical expressions of globally exponentially attracting sets derived, but the existence of a pair of orbits heteroclinic to S 0 and S ± is also proven with the aid of a Lyapunov function and the definitions of both the α -limit set and ω -limit set. Moreover, numerical examples are used to justify the theoretical analysis. Since the obtained results improve and complement the existing ones, they may provide support in chaos control, chaos synchronization, the Hausdorff and Lyapunov dimensions of strange attractors, etc.

Suggested Citation

  • Guiyao Ke, 2024. "Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed," Mathematics, MDPI, vol. 12(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1780-:d:1410828
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