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Tracking problem of the Julia set for the SIS model with saturated treatment function under noise

Author

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  • Liu, Tongtao
  • Zhang, Yongping

Abstract

The tracking problem of Julia sets of the SIS (Susceptible–Infectious–Susceptible) model with saturated healing function under noise perturbation is investigated. Firstly, a discrete version of the SIS model with saturated healing function and its Julia set are introduced. Secondly, the structure of the Julia set are discussed, and the result shows that the filled-in Julia set of this model can be presented as a bounded set with positive measure and an unbounded set. The numerical result shows that the measure of the latter is almost zero. Then, the tracking problem of the Julia sets for the SIS model with saturated healing function is proposed. To address this problem, differential dynamic programming (DDP) and model predictive control (MPC) are used to design controllers. Controllers with different objective functions are compared across their performance. At last, a metric for evaluating the tracking performance is suggested, and a more effective objective function is proposed based on this metric.

Suggested Citation

  • Liu, Tongtao & Zhang, Yongping, 2024. "Tracking problem of the Julia set for the SIS model with saturated treatment function under noise," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924007732
    DOI: 10.1016/j.chaos.2024.115221
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