Large time behavior of nonautonomous differential systems modeling antibiotic-resistant bacteria in rivers

Imene Meriem Mostefaoui; Ali Moussaoui; Sara Jabbari

doi:10.1002/mma.8854

Large time behavior of nonautonomous differential systems modeling antibiotic-resistant bacteria in rivers

Imene Meriem Mostefaoui^*, Ali Moussaoui, Sara Jabbari

^*Corresponding author for this work

Mathematics

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Abstract

In this paper, we study a general nonautonomous model for bacterial dynamics in rivers. The mathematical model is represented by a nonautonomous system of nonlinear ordinary differential equations. We show the existence of a bounded positive invariant and attracting set. By using the Lyapunov function method, we establish global stability of steady-state solutions of the associated autonomous system. Second, the existence of positive periodic solutions of the nonautonomous system is proven using a continuation theorem based on coincidence degree theory.

Original language	English
Journal	Mathematical Methods in the Applied Sciences
Early online date	17 Nov 2022
DOIs	https://doi.org/10.1002/mma.8854
Publication status	E-pub ahead of print - 17 Nov 2022

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This is the peer reviewed version of the following article: (see citation), which has been published in final form at https://doi.org/10.1002/mma.8854. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
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abstract = "In this paper, we study a general nonautonomous model for bacterial dynamics in rivers. The mathematical model is represented by a nonautonomous system of nonlinear ordinary differential equations. We show the existence of a bounded positive invariant and attracting set. By using the Lyapunov function method, we establish global stability of steady-state solutions of the associated autonomous system. Second, the existence of positive periodic solutions of the nonautonomous system is proven using a continuation theorem based on coincidence degree theory.",

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AB - In this paper, we study a general nonautonomous model for bacterial dynamics in rivers. The mathematical model is represented by a nonautonomous system of nonlinear ordinary differential equations. We show the existence of a bounded positive invariant and attracting set. By using the Lyapunov function method, we establish global stability of steady-state solutions of the associated autonomous system. Second, the existence of positive periodic solutions of the nonautonomous system is proven using a continuation theorem based on coincidence degree theory.

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Large time behavior of nonautonomous differential systems modeling antibiotic-resistant bacteria in rivers

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