Competition of Species with Intra-Specific Competition

Abstract

Intra-specific competition in population dynamics can be described by integro-differen- tial equations where the integral term corresponds to nonlocal consumption of resources by in- dividuals 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 pro- cess of speciation, in particular, the emergence of biological species during evolution (6), (7). 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 influ- ence 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.