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Julia Sets and Their Control of Discrete Fractional SIRS Models

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  • Miao Ouyang
  • Yongping Zhang

Abstract

It is of crucial significance to study infectious disease phenomenon by using the discrete SIRS model with the Caputo deltas sense and fractal viewpoint. In this paper, Julia set of the discrete fractional SIRS model is established to analyze the fractal dynamics of this model. Then three different controllers, which are, respectively, added to different parts of the model as a whole, a part, and a product factor, are designed to change the Julia set, and the graphs illustrate the complexity of the model. Simulation results show the efficacy of these methods.

Suggested Citation

  • Miao Ouyang & Yongping Zhang, 2019. "Julia Sets and Their Control of Discrete Fractional SIRS Models," Complexity, Hindawi, vol. 2019, pages 1-10, June.
    • Handle: RePEc:hin:complx:5059025
    DOI: 10.1155/2019/5059025
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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    2. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
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    Cited by:

    1. Lu, Xiaoling & Sun, Weihua, 2024. "Control and synchronization of Julia sets of discrete fractional Ising models," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Zhang, Zizhen & Rahman, Ghaus ur & Gómez-Aguilar, J.F. & Torres-Jiménez, J., 2022. "Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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