Uniform Persistence, Periodicity and Extinction in a Delayed Biological System with Stage Structure and Density-Dependent Juvenile Birth Rate

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.

Stability and bifurcation analysis in a single-species stage structure system with Michaelis–Menten-type harvesting

“…During the last decade, many scholars have studied the stage structure model of species (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and references therein), and many interesting characteristic features of the stage structure model were obtained.…”

“…In ecosystems, maturation, pregnancy, and hunting always occur. Therefore, considering the time delay due to pregnancy effect on the growth of the predator, Zhang and Zhang [6] studied the stage structure model with time delay and density-dependent juvenile birth rate, and they gave conditions for uniform persistence and extinction of the system in the following model:…”