Spatiotemporal patterns in a diffusive predator--prey system with
Leslie--Gower term and social behavior for the prey
- Fethi SOUNA,
- Abdelkader LAKMECHE
Abdelkader LAKMECHE
University of Djillali Liabes Sidi Bel Abbes
Author ProfileAbstract
In this paper, we deal with a new approximation of a diffusive
predator--prey model with Leslie--Gower term and social behavior for the
prey subject to Neumann boundary conditions. A new approach for a
predator-prey interaction in the presence of prey social behavior has
been considered. Our main topic in this work is to study the influence
of the prey's herd shape on the predator-prey interaction in the
presence of Leslie--Gower term. First of all, we examine briefly the
system without spatial diffusion. By analyzing the distribution of the
eigenvalues associated with the constant equilibria, the local stability
of the equilibrium points and the existence of Hopf bifurcation have
been investigated. Then, the spatiotemporal dynamics introduced by self
diffusion was determined, where the existence of the positive solution,
Hopf bifurcation, Turing driven instability, Turing-Hopf bifurcation
point have been derived. Further, the effect of the prey's herd shape
rate on the prey and predator equilibrium densities as well as on the
Hopf bifurcating points has been discussed. Finally, by using the normal
form theory on the center manifold, the direction and stability of the
bifurcating periodic solutions have also been obtained. To illustrate
the theoretical results, some graphical representations are given.14 Oct 2020Submitted to Mathematical Methods in the Applied Sciences 21 Oct 2020Submission Checks Completed
21 Oct 2020Assigned to Editor
27 Oct 2020Reviewer(s) Assigned
08 Feb 2021Review(s) Completed, Editorial Evaluation Pending
17 Feb 2021Editorial Decision: Revise Major
27 Feb 20211st Revision Received
27 Feb 2021Submission Checks Completed
27 Feb 2021Assigned to Editor
01 Mar 2021Reviewer(s) Assigned
06 Jun 2021Review(s) Completed, Editorial Evaluation Pending
08 Jun 2021Editorial Decision: Accept
Dec 2021Published in Mathematical Methods in the Applied Sciences volume 44 issue 18 on pages 13920-13944. 10.1002/mma.7666