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Global studies on a continuous planar piecewise linear differential system with three zones

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Abstract

This paper is concerned with the global dynamics of a continuous planar piecewise linear differential system with three zones, where the dynamic of the one of the exterior linear zones is saddle and the remaining one is anti-saddle. We give all global phase portraits in the Poincaré disc and the complete bifurcation diagram including boundary equilibrium bifurcation curves, degenerate boundary equilibrium bifurcation curves, homoclinic bifurcation curves and double limit cycle bifurcation curves. Its application in a second-order memristor oscillator is shown. Finally, some numerical phase portraits are demonstrated to illustrate our theoretical results.

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Acknowledgements

The authors are very grateful to the anonymous reviewers for their valuable comments and suggestions that greatly improve the presentation and mathematics of this paper. The paper is supported partially by the National Natural Science Foundation of China (No. 62173092, 12171485).

Funding

The paper is supported by the National Natural Science Foundation of China (Nos. 62173092, 12171485).

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Authors and Affiliations

  1. Center for Discrete Mathematics, Fuzhou University, Fuzhou, 350116, Fujian, People’s Republic of China

    Man Jia

  2. School of Mathematics and Statistics, Fuzhou University, Fuzhou, 350116, Fujian, People’s Republic of China

    Man Jia

  3. College of Computer and Date Science, Fuzhou University, Fuzhou, 350116, Fujian, People’s Republic of China

    Youfeng Su

  4. School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Hebai Chen

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  1. Man Jia
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Correspondence to Youfeng Su.

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Jia, M., Su, Y. & Chen, H. Global studies on a continuous planar piecewise linear differential system with three zones. Nonlinear Dyn 111, 3539–3573 (2023). https://doi.org/10.1007/s11071-022-08005-1

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