Journal
CHAOS SOLITONS & FRACTALS
Volume 140, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2020.110180
Keywords
Herd behavior; Predator-prey model; Hopf bifurcation; Turing driven instability; Global stability; Quadratic predator harvesting
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Funding
- DGRSDT of Algeria
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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. (c) 2020 Elsevier Ltd. All rights reserved.
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