[Bifurcations dans un système prédateur-proie avec réponse fonctionnelle non-monotone]
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.
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@article{CRMATH_2005__341_10_601_0,
author = {Broer, H.W. and Naudot, Vincent and Roussarie, Robert and Saleh, Khairul},
title = {Bifurcations of a predator-prey model with non-monotonic response function},
journal = {Comptes Rendus. Math\'ematique},
pages = {601--604},
publisher = {Elsevier},
volume = {341},
number = {10},
year = {2005},
doi = {10.1016/j.crma.2005.09.033},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.09.033/}
}
TY - JOUR AU - Broer, H.W. AU - Naudot, Vincent AU - Roussarie, Robert AU - Saleh, Khairul TI - Bifurcations of a predator-prey model with non-monotonic response function JO - Comptes Rendus. Mathématique PY - 2005 SP - 601 EP - 604 VL - 341 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.09.033/ DO - 10.1016/j.crma.2005.09.033 LA - en ID - CRMATH_2005__341_10_601_0 ER -
%0 Journal Article %A Broer, H.W. %A Naudot, Vincent %A Roussarie, Robert %A Saleh, Khairul %T Bifurcations of a predator-prey model with non-monotonic response function %J Comptes Rendus. Mathématique %D 2005 %P 601-604 %V 341 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.09.033/ %R 10.1016/j.crma.2005.09.033 %G en %F CRMATH_2005__341_10_601_0
Broer, H.W.; Naudot, Vincent; Roussarie, Robert; Saleh, Khairul. Bifurcations of a predator-prey model with non-monotonic response function. Comptes Rendus. Mathématique, Tome 341 (2005) no. 10, pp. 601-604. doi : 10.1016/j.crma.2005.09.033. http://archive.numdam.org/articles/10.1016/j.crma.2005.09.033/
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