Self-localized states in species competition

Paulau, Pavel V.; Gomila, Damià; López, Cristóbal; Hernández-García, Emilio
Physical Review E 89, 032724 (1-8) (2014)

We study the conditions under which species interaction, as
described by continuous versions of the competitive
Lotka-Volterra model (namely the nonlocal Kolmogorov-Fisher
model, and its differential approximation), can support the existence of
localized states, i.e. patches of species with enhanced
population surrounded in niche space by species at smaller
densities. These states would arise from species interaction,
and not by any preferred niche location or better fitness. In
contrast to previous works we include only quadratic
nonlinearities, so that the localized patches appear on a
background of homogeneously distributed species coexistence,
instead than on top of the no-species empty state. For the
differential model we find and describe in detail the stable localized
states. For the full nonlocal model, however competitive
interactions alone do not allow the conditions for the
observation of self-localized states, and we show how the
inclusion of additional facilitative interactions lead to the
appearance of them.

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