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Stability, bifurcation and chaos of a discrete-time pair approximation epidemic model on adaptive networks

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  • Wang, Xinhe
  • Wang, Zhen
  • Lu, Junwei
  • Meng, Bo

Abstract

Adaptive behavior on networks leads to bifurcation and other special phenomenon, which has been proved for differential systems. In this paper, one will discuss the stability, bifurcation and chaos of the discrete pair epidemic model on adaptive networks, which will bring some new challenges. The stability of the disease free equilibrium and endemic equilibrium with respect to basic reproduction number R0 is studied. Under certain conditions, as the time step-size increases, flip bifurcation that occurs at the endemic equilibrium is discussed, the period-doubling bifurcation and the chaos phenomenon of the system are exhibited, some figures are provided for illustration. According to the results in this paper, the dynamical behaviors of the discrete model are multitudinous and quite different from the continuous model.

Suggested Citation

  • Wang, Xinhe & Wang, Zhen & Lu, Junwei & Meng, Bo, 2021. "Stability, bifurcation and chaos of a discrete-time pair approximation epidemic model on adaptive networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 182-194.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:182-194
    DOI: 10.1016/j.matcom.2020.10.019
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
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    Cited by:

    1. Wang, Xinhe & Wang, Zhen, 2022. "Bifurcation and propagation dynamics of a discrete pair SIS epidemic model on networks with correlation coefficient," Applied Mathematics and Computation, Elsevier, vol. 435(C).

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