Portal de Periódicos da CAPES

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

2019; American Institute of Mathematical Sciences; Volume: 24; Issue: 9 Linguagem: Inglês

10.3934/dcdsb.2019042

1553-524X

Safia Slimani, Paul Raynaud de Fitte, Islam Boussaada,

Mathematical Biology Tumor Growth

We study a modified version of a prey-predator system with modified Leslie-Gower and Holling type Ⅱ functional responses 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.