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

Safia Slimani (1) , Paul Raynaud de Fitte (1) , Islam Boussaada (2, 3, 4)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 L2S - Laboratoire des signaux et systèmes
3 IPSA - Institut Polytechnique des Sciences Avancées
4 DISCO - Dynamical Interconnected Systems in COmplex Environments

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]

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⟩