Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting

• Published in: Chaos, solitons and fractals Vol. 140; p. 110180
• Main Authors: Souna, Fethi, Lakmeche, Abdelkader, Djilali, Salih
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2020
• Subjects: Global stability; Herd behavior; Hopf bifurcation; Predator-prey model; Quadratic predator harvesting; Turing driven instability; 34D23; 35F10; 92D25; Global stability; Quadratic predator harvesting; Herd behavior; Turing driven instability; 35B40; Hopf bifurcation; Predator-prey model
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2020.110180

•A predator-prey model with prey protection zone and predator harvesting is investigated.•Existence, positivity, uniqueness of solution is shown.•The existence and uniqueness of the positive homogeneous steady state is proved.•Global stability of the boundary equilibrium steady state is investigated under some value of model parameters.•The existence of Hopf, Turing, Turing-Hopf bifurcations is investigated.•The stability of the periodic solutions are studied using the normal form.•Some numerical simulations are used for discussing the impact of the predator harvesting on the spatiotemporal behavior of solution. In this paper, a diffusive predator-prey model subject to the zero flux boundary conditions is considered, in which the prey population exhibits social behavior and the harvesting functional of the predator population is assumed to be considered in a quadratic form. The existence of a positive solution and its bounders is investigated. The global stability of the semi trivial constant equilibrium state is established. Concerning the non trivial equilibrium state, the local stability, Hopf bifurcation, diffusion driven instability, Turing-Hopf bifurcation are investigated. The direction and the stability of Hopf bifurcation relying on the system parameters is derived. Some numerical simulations are used to extend the analytical results and show the occurrence of the homogeneous and non homogeneous periodic solutions. Further the effect of the rivalry rate on the dynamical behavior of the studied species.