1,082 research outputs found
Population Growth and Competition Models with Decay and Competition Consistent Delay
We derive an alternative expression for a delayed logistic equation in which
the rate of change in the population involves a growth rate that depends on the
population density during an earlier time period. In our formulation, the delay
in the growth term is consistent with the rate of instantaneous decline in the
population given by the model. Our formulation is a modification of [Arino et
al., J.~Theoret.~Biol.~241(1):109--119, 2006] by taking the intraspecific
competition between the adults and juveniles into account. We provide a
complete global analysis showing that no sustained oscillations are possible. A
threshold giving the interface between extinction and survival is determined in
terms of the parameters in the model. The theory of chain transitive sets and
the comparison theorem for cooperative delay differential equations are used to
determine the global dynamics of the model.
We extend our delayed logistic equation to a system modeling the competition
of two species. For the competition model, we provide results on local
stability, bifurcation diagrams, and adaptive dynamics. Assuming that the
species with shorter delay produces fewer offspring at a time than the species
with longer delay, we show that there is a critical value, , such that
the evolutionary trend is for the delay to approach .Comment: 22 pages, 6 figures, 1 tabl
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