TITLE:
Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate
AUTHORS:
Limin Zhang, Chaofeng Zhang
KEYWORDS:
Uniform Persistence, Periodicity, Extinction, Density Dependence, Stage Structure
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.6 No.2,
June
20,
2016
ABSTRACT: A
delayed biological system of predator-prey interaction with stage structure and
density dependent juvenile birth rate is investigated. It is assumed that the prey
population has two stages: immature and mature. The growth of the immature prey
is density dependent and is a function of the density of adult prey. Such phenomenon
has been reported for beetles, tribolium, copepods, scorpions, several fish species
and even crows. The growth of the predator is affected by the time delay due to
gestation. By some Lemmas and methods of delay differential equation, the conditions
for the uniform persistence and extinction of the system are obtained. Numerical
simulations illustrate the feasibility of the main results and demonstrate that
the density dependent coefficient has influence on the system populations’ densities
though it has no effect on uniform persistence and extinction of the system.