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Hopf bifurcation and fixed-time stability of a reaction–diffusion echinococcosis model with mixed delays

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  • Chen, Weixin
  • Xu, Xinzhong
  • Zhang, Qimin

Abstract

In this paper, a model with spatial diffusion and mixed delays is presented to describe the spread of echinococcosis between dogs and livestock. Firstly, the local stability is investigated using the Routh–Hurwitz criterion. Furthermore, when considering time delays as bifurcation parameters, the conditions for the occurrence of Hopf bifurcation are discussed based on the linear approximation of the nonlinear system. Lastly, the fixed-time stability is studied under the implementation of appropriate control measures. Numerical simulations are provided to give a better understanding of the theoretical results.

Suggested Citation

  • Chen, Weixin & Xu, Xinzhong & Zhang, Qimin, 2024. "Hopf bifurcation and fixed-time stability of a reaction–diffusion echinococcosis model with mixed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 1-19.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:1-19
    DOI: 10.1016/j.matcom.2024.04.002
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    References listed on IDEAS

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    1. Kai Wang & Xueliang Zhang & Zhidong Teng & Lei Wang & Liping Zhang, 2014. "Analysis of a Patch Model for the Dynamical Transmission of Echinococcosis," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, March.
    2. Zhu, Guanghu & Chen, Sixing & Shi, Benyun & Qiu, Hongjun & Xia, Shang, 2019. "Dynamics of echinococcosis transmission among multiple species and a case study in Xinjiang, China," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 103-109.
    3. Li, Ruoxia & Cao, Jinde & Alsaedi, Ahmad & Alsaadi, Fuad, 2017. "Exponential and fixed-time synchronization of Cohen–Grossberg neural networks with time-varying delays and reaction-diffusion terms," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 37-51.
    4. Ebrahimi Dehshalie, Maziar & Kabiri, Meisam & Ebrahimi Dehshali, Mahyar, 2021. "Stability analysis and fixed-time control of credit risk contagion," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 131-139.
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