Refuge used by prey as a function of predator numbers in a Leslie-type model

Abstract

This paper deals with a continuous-time predator-prey model of Leslie-Gower type considering the use of a physical refuge by a fraction of the prey population. The fraction of hidden prey is assumed to be dependent on the presence of predators in the environment. The conditions for the existence of equilibrium points and their local stability are established. In particular, it is shown that the point (0; 0) has a great importance in the dynamics of the model, since it determines a separating curve Σ that divides the behavior of the trajectories. Those trajectories that are above this curve have as their w- limit the point (0; 0), so the extinction of both populations may be possible depending on the initial conditions.

Keywords

• predator-prey model
• refuge
• stability
• bifurcations
• limit cycles
• separatrix curves