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A generalized feedback control model for the logistic differential equation

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Abstract

In this work, we introduce and study a new and generalized feedback control model for the logistic differential equation. Dynamical qualitative properties of the feedback control model are analyzed rigorously. By combining the Lyapunov stability theory with characteristics of negative definite quadratic forms, the global stability asymptotic stability (GAS) of the proposed model is established. Also, a comparison between the original logistic equation and the feedback control model is given. As an important consequence, we conclude that the feedback control variables do not affect the GAS but only change the position (value) of the (positive) unique equilibrium point of the original logistic equation. The proposed model improves some previously recognized works and can be extended in the context of fractional-order derivative operators, time delay and discrete time. Finally, numerical experiments are performed to support the theoretical assertions.

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Authors and Affiliations

  1. Department of Mathematics, FPT University, Hoa Lac Hi-Tech Park, Km29 Thang Long Blvd, Hanoi, Viet Nam

    Manh Tuan Hoang

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  1. Manh Tuan Hoang
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Manh Tuan Hoang involved in conceptualization, methodology, software, formal analysis, writing—original draft preparation, methodology, writing—review , editing and supervision.

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Correspondence to Manh Tuan Hoang.

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Hoang, M.T. A generalized feedback control model for the logistic differential equation. Int. J. Dynam. Control 11, 2265–2272 (2023). https://doi.org/10.1007/s40435-022-01108-y

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  • DOI: https://doi.org/10.1007/s40435-022-01108-y

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