NOUSSAIR, Ahmed; AINSEBA, Bedr'Eddine; BENDAHMANE, Mostafa

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NOUSSAIR, Ahmed
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

AINSEBA, Bedr'Eddine
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

BENDAHMANE, Mostafa
Centro de Investigación en Ingeniería Matemática [Concepción] [CI²MA]

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Nonlinear Analysis: Real World Applications. 2008-12-04, vol. 9, n° 5, p. 2086-2105

Elsevier

Resumen en inglés

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.< Leer menos

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Reaction–diffusion system

Predator–prey

Prey-taxis

Finite volume scheme

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

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