# American Institute of Mathematical Sciences

May  2009, 11(3): 541-561. doi: 10.3934/dcdsb.2009.11.541

## Travelling waves for integro-differential equations in population dynamics

 1 Department of Mathematics, Technical University of Iasi, Iasi, Romania 2 IMB & INRIA sud-ouest Anubis, Université de Bordeaux, France 3 Institute of Mathematics, University Lyon 1, 69622 Villeurbann, France

Received  December 2007 Revised  October 2008 Published  March 2009

The paper is devoted to integro-differential equations arising in population dynamics. The integral term describes the nonlocal consumption of resources. We study the Fredholm property of the corresponding linear operators and use it to prove the existence of travelling waves when the support of the integral is sufficiently small. In this case, the integro-differential operator is close to the differential operator and we can use the implicit function theorem. We carry out numerical simulations in order to study the case where the support of the integral is not small. We observe various regimes of wave propagation. Some of them, in particular periodic waves do not exist for the usual reaction-diffusion equation.
Citation: Narcisa Apreutesei, Arnaud Ducrot, Vitaly Volpert. Travelling waves for integro-differential equations in population dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 11 (3) : 541-561. doi: 10.3934/dcdsb.2009.11.541
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