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Discontinuity, Nonlinearity, and Complexity 8(3) (2019) 325--340 | DOI:10.5890/DNC.2019.09.008

A. Moussaoui$^{1}$, M. A. Aziz Alaoui$^{2}$

$^{1}$ Department of Mathematics, Faculty of Sciences, University of Tlemcen, Algeria

$^{2}$ Normandie Univ, France; ULH, LMAH, F-76600 Le Havre, FR CNRS 3335, ISCN, 25 rue Philippe Lebon 76600 Le Havre, France

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Abstract

In this paper we develop a non-autonomous predator-prey system with time delay to study the influence of water level fluctuations on the interactions between fish species living in an artificial lake. We derive persistence and extinction conditions of the species. Using coincidence degree theory, we determine conditions for which the system has at least one periodic solution. Numerical simulations are presented to illustrate theoretical results.

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