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Volume 8,     Number 3,     Fall 2000

 

ANALYSIS OF A TWO-STAGE POPULATION MODEL WITH SPACE LIMITATIONS AND STATE-DEPENDENT DELAY
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.

 

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