Competition of Species with Intra-Specific Competition

Abstract

Intra-specific competition in population dynamics can be described by integro-differentialequations where the integral term corresponds to nonlocal consumption of resources by individualsof the same population. Already the single integro-differential equation can show theemergence of nonhomogeneous in space stationary structures and can be used to model the processof 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)]. Onthe other hand, competition of two different species represents a well known and well studiedmodel in population dynamics. In this work we study how the intra-specific competition can influencethe competition between species. We will prove the existence of travelling waves for the casewhere the support of the kernel of the integral is sufficiently narrow. Numerical simulations willbe carried out in the case of large supports.