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Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes

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  • Tuan Hoang, Manh
  • Nagy, A.M.

Abstract

In this paper, we propose and study a Logistic model with feedback control of fractional order that is extended directly from a system of ordinary differential equations. Uniform asymptotic stability of this model is established based on an appropriate Lyapunov function and an important consequence of this result; we present a simple proof for the global stability of the original system of ordinary differential equations. Besides, to numerically solve and simulate the proposed fractional model, unconditionally positive nonstandard finite difference schemes are constructed and analyzed. Finally, the numerical simulations obtained by the constructed nonstandard finite difference schemes are compared with the Grunwald–Letnikov scheme to reveal that the proposed scheme is convenient for solving the proposed model and confirm the validity of the established results.

Suggested Citation

  • Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:24-34
    DOI: 10.1016/j.chaos.2019.03.031
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    References listed on IDEAS

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    Cited by:

    1. Avcı, İbrahim & Hussain, Azhar & Kanwal, Tanzeela, 2023. "Investigating the impact of memory effects on computer virus population dynamics: A fractal–fractional approach with numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
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    3. Hoang, Manh Tuan, 2022. "Positivity and boundedness preserving nonstandard finite difference schemes for solving Volterra’s population growth model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 199(C), pages 359-373.
    4. Hoang, Manh Tuan, 2023. "Dynamical analysis of a generalized hepatitis B epidemic model and its dynamically consistent discrete model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 291-314.

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