IJPAM: Volume 70, No. 2 (2011)
WITH A CONSTANT INFLOW OF NEWBORNS: THE CASE
WHEN THE DEATH RATE DEPENDS ON JUVENILES ONLY
AND THE GROWTH RATE DEPENDS ON SIZE ONLY AND
THE CASE WHEN BOTH RATES DEPEND ON SIZE ONLY
Faculty of Mathematical Sciences
University of Khartoum
P.O. Box 321, Khartoum, SUDAN
Abstract. The stability of a size-structured population model is investigated when the population is divided into adults and juveniles, and there is a constant inflow of newborns from an external source. We concentrate our efforts in two special cases, the first is when the death rate depends on juveniles only and the growth rate depends on size only, and, the second is when both the death rate and the growth rate depend on size only. In both special cases we assume that the maximum size for an individual in the population is infinite, and that there is an inflow of newborns from an external source. We identify three demographic parameters and show that they determine sufficient conditions for the (in)stability of a nontrivial steady state. We also give examples that illustrate the stability results. The results in this paper generalize previous results, for example, see Calsina, et al. (2003), El-Doma (2006), El-Doma (2008 a), El-Doma (2008 b), and El-Doma (2009).
Received: April 17, 2011
AMS Subject Classification: 45M10, 35B35, 35L60, 92D25
Key Words and Phrases: population, adults, juveniles, stability, steady state, size-structure
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395