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Research Article | Open Access

Almost periodic solutions of a discrete Lotka-Volterra model via exponential dichotomy theory

Lini Fang, N'gbo N'gbo, Yonghui Xia( )
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
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Abstract

In this paper, we consider a discrete non-autonomous Lotka-Volterra model. Under some assumptions, we prove the existence of positive almost periodic solutions. Our analysis relies on the exponential dichotomy for the difference equations and the Banach fixed point theorem. Furthermore, by constructing a Lyapunov function, the exponential convergence is proved. Finally, a numerical example illustrates the effectiveness of the results.

Keywords

almost periodic solutiondifference exponential dichotomyBanach fixed pointdiscrete Lotka-Volterra modelexponential convergence
CLC number: 34D10, 34K14, 39A10, 39A11

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 3788-3801
DOI: 10.3934/math.2022210

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Cite this article:
Fang L, N'gbo N, Xia Y. Almost periodic solutions of a discrete Lotka-Volterra model via exponential dichotomy theory. AIMS Mathematics, 2022, 7(3): 3788-3801. https://doi.org/10.3934/math.2022210

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Received: 03 October 2021
Accepted: 01 December 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)