Bifurcations of a predator-prey model with non-monotonic response function

H.W. Broer; Vincent Naudot; Robert Roussarie; Khairul Saleh

doi:10.1016/j.crma.2005.09.033

Ordinary Differential Equations

Bifurcations of a predator-prey model with non-monotonic response function
[Bifurcations dans un système prédateur-proie avec réponse fonctionnelle non-monotone]

Présenté par : Étienne Ghys

H.W. Broer ¹ ; Vincent Naudot ¹ ; Robert Roussarie ² ; Khairul Saleh ¹

¹ University of Groningen, Department of Mathematics, P.O. Box 800, NL-9700 AV Groningen, The Netherlands
² Institut mathématiques de Bourgogne, 9, avenue Alain-Savary, B.P. 47870, 21078 Dijon cedex, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, pp. 601-604.

Résumé
Abstract

On considère un modèle prédateur-proie en dimension 2 dépendant de cinq paramètres adapté du système Volterra–Lotka par une réponse fonctionnelle non-monotone. Une description des différents domaines de stabilité structurelle est présentée ainsi que leurs bifurcations. La structure de l'ensemble de bifurcation se réduit à quatre centres organisateurs de codimension 3. Nous présentons quelques examples d'attracteurs étranges obtenus par une pertubation périodique non autonome.

A 2-dimensional predator-prey model with five parameters is investigated, adapted from the Volterra–Lotka system by a non-monotonic response function. A description of the various domains of structural stability and their bifurcations is given. The bifurcation structure is reduced to four organising centres of codimension 3. Research is initiated on time-periodic perturbations by several examples of strange attractors.

Reçu le : 2005-06-30
Accepté le : 2005-09-11
Publié le : 2005-10-26

DOI : 10.1016/j.crma.2005.09.033

Affiliations des auteurs :

H.W. Broer ¹ ; Vincent Naudot ¹ ; Robert Roussarie ² ; Khairul Saleh ¹

¹ University of Groningen, Department of Mathematics, P.O. Box 800, NL-9700 AV Groningen, The Netherlands
² Institut mathématiques de Bourgogne, 9, avenue Alain-Savary, B.P. 47870, 21078 Dijon cedex, France

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H.W. Broer; Vincent Naudot; Robert Roussarie; Khairul Saleh. Bifurcations of a predator-prey model with non-monotonic response function. Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, pp. 601-604. doi : 10.1016/j.crma.2005.09.033. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.033/

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H.W. Broer; Vincent Naudot; Robert Roussarie; Khairul Saleh Bifurcations of a predator-prey model with non-monotonic response function, Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, p. 601 | DOI:10.1016/j.crma.2005.09.033

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