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.

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.

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.

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 
@article{CRMATH_2007__345_4_199_0,
     author = {Mostafa Fazly and Mahmoud Hesaaraki},
     title = {Periodic solutions for a discrete time predator{\textendash}prey system with monotone functional responses},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {199--202},
     publisher = {Elsevier},
     volume = {345},
     number = {4},
     year = {2007},
     doi = {10.1016/j.crma.2007.06.021},
     language = {en},
}
TY  - JOUR
AU  - Mostafa Fazly
AU  - Mahmoud Hesaaraki
TI  - Periodic solutions for a discrete time predator–prey system with monotone functional responses
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 199
EP  - 202
VL  - 345
IS  - 4
PB  - Elsevier
DO  - 10.1016/j.crma.2007.06.021
LA  - en
ID  - CRMATH_2007__345_4_199_0
ER  - 
%0 Journal Article
%A Mostafa Fazly
%A Mahmoud Hesaaraki
%T Periodic solutions for a discrete time predator–prey system with monotone functional responses
%J Comptes Rendus. Mathématique
%D 2007
%P 199-202
%V 345
%N 4
%I Elsevier
%R 10.1016/j.crma.2007.06.021
%G en
%F CRMATH_2007__345_4_199_0
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/

[1] M. Bohner; M. Fan; J. Zhang Existence of periodic solutions in predator–prey and competition dynamic systems, Nonlinear Anal.: Real World Appl., Volume 7 (2006), pp. 1193-1204

[2] M. Fan; Q. Wang Periodic solutions of a class of nonautonomous discrete time semi-ratio-dependent predator–prey systems, Discrete Contin. Dyn. Syst. Ser. B, Volume 4 (2004) no. 3, pp. 563-574

[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

[4] H.I. Freedman Deterministic Mathematical Models in Population Ecology, Monograph Textbooks Pure Applied Math., vol. 57, Marcel Dekker, New York, 1980

[5] R.E. Gaines; J.L. Mawhin Coincidence Degree and Non-Linear Differential Equations, Springer, Berlin, 1977

[6] Q. Wang; M. Fan; K. Wang Dynamics of a class of nonautonomous semi-ratio-dependent predator–prey systems with functional responses, J. Math. Anal. Appl., Volume 278 (2003), pp. 443-471

Cité par Sources :

Commentaires - Politique