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

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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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    1. Varma, Rashmi & Sushil,, 2019. "Bridging the electricity demand and supply gap using dynamic modeling in the Indian context," Energy Policy, Elsevier, vol. 132(C), pages 515-535.
    2. Barman, Madhab & Mishra, Nachiketa, 2024. "Hopf bifurcation analysis for a delayed nonlinear-SEIR epidemic model on networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. Zheng, Qianqian & Shen, Jianwei & Pandey, Vikas & Guan, Linan & Guo, Yantao, 2023. "Turing instability in a network-organized epidemic model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
    5. Shu, Jingsi & Zhang, Yongping, 2023. "Fractal control and synchronization of population competition model based on the T–S fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Khajanchi, Subhas & Bera, Sovan & Roy, Tapan Kumar, 2021. "Mathematical analysis of the global dynamics of a HTLV-I infection model, considering the role of cytotoxic T-lymphocytes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 354-378.
    7. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "The impact of the media awareness and optimal strategy on the prevalence of tuberculosis," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    8. Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    9. Das, Dhiraj Kumar & Khajanchi, Subhas & Kar, T.K., 2020. "Transmission dynamics of tuberculosis with multiple re-infections," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    10. Wang, Yupin & Liu, Shutang & Li, Hui & Wang, Da, 2019. "On the spatial Julia set generated by fractional Lotka-Volterra system with noise," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 129-138.
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