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

Manh Tuan Hoang and A.M. Nagy

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 24-34

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.

Keywords: Logistic model; Feedback controls; Fractional differential equations; Lyapunov function; Nonstandard finite difference schemes; Global stability (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:24-34

DOI: 10.1016/j.chaos.2019.03.031

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