Dynamics of a prey-predator system with modified Leslie-Gower and Holling type II schemes incorporating a prey refuge

We study a modified version of a prey-predator system with modified Leslie-Gower and Holling type II functional response studied by M.A. Aziz-Alaoui and M. Daher-Okiye. The modification consists in incorporating a refuge for preys, and substantially complicates the dynamics of the system. We study the local and global dynamics and the existence of cycles. We also investigate conditions for extinction or existence of a stationary distribution, in the case of a stochastic perturbation of the system.

Mots clés

extinction refuge Poincaré index theorem Holling type II Prey-predator Leslie-Gowers ergodic er-godic 1 stationary distribution stochastic differential persistence Leslie-Gower

Domaines

Probabilités [math.PR] Systèmes dynamiques [math.DS]

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proie-predateur-HAL.pdf (1 Mo)

Origine	Fichiers produits par l'(les) auteur(s)

Paul Raynaud de Fitte : Connectez-vous pour contacter le contributeur

https://hal.science/hal-01707650

Soumis le : mercredi 16 janvier 2019-18:30:03

Dernière modification le : jeudi 28 novembre 2024-15:08:02

Dates et versions

hal-01707650 , version 1 (15-02-2018)

hal-01707650 , version 2 (19-05-2018)

hal-01707650 , version 3 (04-10-2018)

hal-01707650 , version 4 (16-01-2019)

Identifiants

HAL Id : hal-01707650 , version 4
ARXIV : 1802.05967

Citer

Safia Slimani, Paul Raynaud de Fitte, Islam Boussaada. Dynamics of a prey-predator system with modified Leslie-Gower and Holling type II schemes incorporating a prey refuge. 2019. ⟨hal-01707650v4⟩

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