DUCROT, Arnaud; GUYONNE, Vincent; LANGLAIS, Michel

doi:10.3934/dcdss.2011.4.67

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

GUYONNE, Vincent
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

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

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Discrete and Continuous Dynamical Systems - Series S. 2011-02, vol. 4, n° 1, p. 67-82

American Institute of Mathematical Sciences

Résumé en anglais

We are interested in the dynamical behaviour of the solution set to a two component reaction–diﬀusion system posed on non coincident spatial do- mains. The underlying biological problem is a predator–prey system featuring a non local numerical response to predation involving an integral kernel. Quite interesting while complex dynamics emerge from preliminary numerical simu- lations, driven both by diﬀusivities and by the parametric form or shape of the integral kernel. We consider a simpliﬁed version of this problem, with constant coeﬃcients, and give some hints on the large time dynamics of solutions.< Réduire

Mots clés en anglais

Reaction-Diﬀusion system

non-coincident spatial domains

stationary solutions

degree theory

persistence

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Some remarks on the qualitative properties of solutions to a predator–prey model posed on non coincident spatial domains

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