Spatiotemporal Complexity of a Leslie-Gower Predator-Prey Model with the Weak Allee Effect

Abstract EN

We investigate a diffusive Leslie-Gower predator-prey model with the additive Allee effect on prey subject to the zero-flux boundary conditions.

Some results of solutions to this model and its corresponding steady-state problem are shown.

More precisely, we give the stability of the positive constant steady-state solution, the refined a priori estimates of positive solution, and the nonexistence and existence of the positive nonconstant solutions.

We carry out the analytical study for two-dimensional system in detail and find out the certain conditions for Turing instability.

Furthermore, we perform numerical simulations and show that the model exhibits a transition from stripe-spot mixtures growth to isolated spots and also to stripes.

These results show that the impact of the Allee effect essentially increases the model spatiotemporal complexity.