Dynamics of a harvested stage‐structured predator–prey model with distributed maturation delay

2021 ◽  
Author(s):  
Jafar Al‐Omari ◽  
Ghaleb Gumah ◽  
Shrideh Al‐Omari
Keyword(s):  
Predator Prey ◽  
Maturation Delay ◽  
Predator Prey Model ◽  
Prey Model

A STAGE-STRUCTURED PREDATOR–PREY MODEL WITH DENSITY-DEPENDENT MATURATION DELAY

2011 ◽  
Vol 04 (03) ◽  
pp. 289-312 ◽  
Author(s):  
MANJU AGARWAL ◽  
SAPNA DEVI
Keyword(s):  
Predator Population ◽  
System Behavior ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Density Dependent ◽  
Maturation Delay ◽  
Predator Prey Model ◽  
Prey Model ◽  
Trivial Equilibrium ◽  
Quantitative Changes

In this paper, a stage-structured predator–prey model is proposed and analyzed with density-dependent maturation delay. We studied the dynamics of our model analytically and obtained conditions which influence the positivity and boundedness of all populations. Criteria for the existence of a non-trivial equilibrium and conditions for the uniqueness of this equilibrium are given. A linearized analysis on the equilibria, which is algebraically very complicated in the case of non-trivial equilibrium, is carried out. We proved that the system is globally asymptotically stable in the situation when non-trivial equilibrium does not exist. To accomplish our all analytical findings and to investigate the effect of density-dependent maturation delay on the system behavior, we presented a numerical simulation. It is concluded that variations in parameter, which we introduce in the system to observe the effect of density-dependent maturation delay, produces significant quantitative changes in system behavior and also qualitative changes in the behavior of immature predator population.

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