Volume 8, Number 3, Fall 2000
ANALYSIS OF A TWO-STAGE POPULATION MODEL
WITH SPACE LIMITATIONS AND
SANJAY RAI AND ROBERT L. ROBERTSON
Abstract. Bence and Nisbet introduced a system of
nonlinear functional differential equations with constant delay
to describe the growth of a population with space limitations.
In their work, the population was divided into two groups:
the juveniles and the adults. They included a local stability
analysis of the system. Kuang and So gave a thorough
mathematical analysis of the system, including results on
positivity, boundedness, and stability of solutions. In this
paper, a more general situation is considered: a system where
the delay is a nonconstant function of total population, and
the death rate of adults is nonlinear. Results on positivity,
boundedness, and stability of solutions are proven.