Comptes Rendus
no. 4
Ordinary Differential Equations
Periodic solutions for a discrete time predator–prey system with monotone functional responses
[Solutions périodiques d'un système discret prédateur–proie du temps avec des réponses fonctionnelles monotones]

Présenté par : Jean-Michel Bony

Mostafa Fazly1 ; Mahmoud Hesaaraki1
1 Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Azadi Ave., Tehran, Iran
Comptes Rendus. Mathématique, Volume 345 (2007) no. 4, pp. 199-202.

Dans cette Note, on donne de nouvelles conditions suffisantes d'existence d'une solution périodique d'un système discret non autonome prédateur–proie, dépendant du temps avec condition semi-finale et pour différentes réponses fonctionnelles. Dans les résultats obtenus, pour des réponses fonctionnelles monotones majorées par des polynômes sur R+, le système a toujours au moins une solution ω-périodique. En particulier, pour les réponses fonctionnelles les plus utilisées – Michaelis–Menten, type-II et III de Holling, sigmoïde, Ivlev et d'autres fonctions monotones – le système a toujours une solution ω-périodique.

In this Note, sharp sufficient conditions for the existence of periodic solutions of a nonautonomous discrete time semi-ratio-dependent predator–prey system with functional responses are derived. In our results this system with any monotone functional response bounded by polynomials in R+, always has at least one ω-periodic solution. In particular, this system with the most popular functional responses Michaelis–Menten, Holling type-II and III, sigmoidal, Ivlev and some other monotone response functions, always has at least one ω-periodic solution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.06.021
Mostafa Fazly 1 ; Mahmoud Hesaaraki 1

1 Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Azadi Ave., Tehran, Iran 
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Mostafa Fazly; Mahmoud Hesaaraki. Periodic solutions for a discrete time predator–prey system with monotone functional responses. Comptes Rendus. Mathématique, Volume 345 (2007) no. 4, pp. 199-202. doi : 10.1016/j.crma.2007.06.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.06.021/

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[3] M. Fazly; M. Hesaaraki Periodic solutions for predator–prey systems with Beddington–DeAngelis functional response on time scales, Nonlinear Anal.: Real World Appl. (2007) | DOI

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