TITLE:
Permanence, Periodicity and Extinction of a Delayed Biological System with Stage-Structured Preference for Predator
AUTHORS:
Limin Zhang, Chaofeng Zhang
KEYWORDS:
Stage-Structured Preference, Permanence, Periodic Solution, Extinction, Time Delay
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.3,
March
29,
2016
ABSTRACT: This study considers a delayed biological system of predator-prey interactions where the predator has stage-structured preference. It is assumed that the prey population has two stages: immature and mature. The predator population has different preference for the stage-structured prey. This type of behavior has been reported in Asecodes hispinarum and Microplitis mediator. By some lemmas and methods of delay differential equation, the conditions for the permanence, existence of positive periodic solution and extinction of the system are obtained. Numerical simulations are presented that illustrate the analytical results as well as demonstrate certain biological phenomena. In particular, overcrowding of the predator does not affect the persistence of the system, but our numerical simulations suggest that overcrowding reduces the density of the predator. Under the assumption that immature prey is easier to capture, our simulations suggest that the predator’s preference for immature prey increases the predator density.