1,132 research outputs found
Coexistence and Segregation for Strongly Competing Species in Special Domains
We deal with strongly competing multispecies systems of Lotka-Volterra type
with homogeneous Dirichlet boundary conditions. For a class of nonconvex
domains composed by balls connected with thin corridors, we show the occurrence
of pattern formation (coexistence and spatial segregation of all the species),
as the competition grows indefinitely. As a result we prove the existence and
uniqueness of solutions for a remarkable system of differential inequalities
involved in segregation phenomena and optimal partition problems
Competition between stable equilibria in reaction-diffusion systems: the influence of mobility on dominance
This paper is concerned with reaction-diffusion systems of two symmetric
species in spatial dimension one, having two stable symmetric equilibria
connected by a symmetric standing front. The first order variation of the speed
of this front when the symmetry is broken through a small perturbation of the
diffusion coefficients is computed. This elementary computation relates to the
question, arising from population dynamics, of the influence of mobility on
dominance, in reaction-diffusion systems modelling the interaction of two
competing species. It is applied to two examples. First a toy example, where it
is shown that, depending on the value of a parameter, an increase of the
mobility of one of the species may be either advantageous or disadvantageous
for this species. Then the Lotka-Volterra competition model, in the bistable
regime close to the onset of bistability, where it is shown that an increase of
mobility is advantageous. Geometric interpretations of these results are given.Comment: 43 pages, 10 figure
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