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Article Dans Une Revue Nonlinear Analysis: Real World Applications Année : 2008

A reaction–diffusion system modeling predator–prey with prey-taxis

Résumé

We are concerned with a system of nonlinear partial differential equations modeling the Lotka–Volterra interactions of predators and preys in the presence of prey-taxis and spatial diffusion. The spatial and temporal variations of the predator's velocity are determined by the prey gradient. We prove the existence of weak solutions by using Schauder fixed-point theorem and uniqueness via duality technique. The linearized stability around equilibrium is also studied. A finite volume scheme is build and numerical simulation show interesting phenomena of pattern formation.
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Dates et versions

hal-00391778 , version 1 (04-06-2009)

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  • HAL Id : hal-00391778 , version 1

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Ahmed Noussair, Bedr'Eddine Ainseba, Mostafa Bendahmane. A reaction–diffusion system modeling predator–prey with prey-taxis. Nonlinear Analysis: Real World Applications, 2008, 9 (5), pp.2086-2105. ⟨hal-00391778⟩
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