Competition of Species with Intra-Specific Competition

¹ Department of Mathematics, Technical University of Iasi, Iasi, Romania
² Institute of Mathematics, University Bordeaux 2, 33076 Bordeaux, France
³ Institute of Mathematics, Université Lyon 1, UMR 5208 CNRS, 69622 Villeurbanne, France

Corresponding author: napreut@net89mail.dntis.ro

Abstract

Intra-specific competition in population dynamics can be described by integro-differential equations where the integral term corresponds to nonlocal consumption of resources by individuals of the same population. Already the single integro-differential equation can show the emergence of nonhomogeneous in space stationary structures and can be used to model the process of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom. 1 (2006), no. 1, 65-82], [S. Genieys et al., Comptes Rendus Biologies, 329 (11), 876-879 (2006)]. On the other hand, competition of two different species represents a well known and well studied model in population dynamics. In this work we study how the intra-specific competition can influence the competition between species. We will prove the existence of travelling waves for the case where the support of the kernel of the integral is sufficiently narrow. Numerical simulations will be carried out in the case of large supports.