DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

QUASIDIFFUSION MODEL OF POPULATION COMMUNITY
F. BEREZOVSKAYA
By methods of qualitative theory of ODE and theory bifurcations we analyze the model
dynamics of the community consisting of “predator-prey” and “prey” systems affected
by prey intermigrations; we suppose that the Allee effect is incorporated in each prey
population. We show that the model community persists with parameter values for which
any “separate” population system can go to extinction. We investigate the dynamics of
coexistence, and in particular show that the model community can either exist in steady
state or with oscillations, or realize extinction depending on initial densities.
Copyright © 2006 F. Berezovskaya. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original work is properly cited.
1. Dynamics of local model with the Allee effect
1.1. Two population models. The Allee effect [1, 10] means that the fertility of a population
depends nonmonotonically on the population size and function of population
growth has maximum and minimum values. The simplest model describing this effect is
u ′ = βf(u) = u(u − l)(1 − u), (1.1)
where u is a normalized population density, l is a parameter satisfying 0 ≤ l ≤ 1. With
0