Abstract
This paper deals with a predator–prey model with both species in the delayed-dispersal case in a two-patch environment. The purpose of this paper is to study the effect of two dispersal delays on the stability of three equilibria. It turns out that the stability of the trivial equilibrium and the boundary equilibrium is delay-independent. However, the stability of the coexistence equilibrium is delay-dependent. Numerical simulations are performed to demonstrate the obtained results.
Highlights
The relationship of predator and prey is prevalent in nature and is one of the most important themes in ecological and mathematical models
Since the Lotka–Volterra predator–prey model was formulated, various predator–prey models have been studied by incorporating additional ecological concepts into the classical Lotka–Volterra model, such as functional responses, dispersal and time delay
We mainly numerically examine how the two dispersal delays affect the stability of the coexistence equilibrium in our model
Summary
The relationship of predator and prey is prevalent in nature and is one of the most important themes in ecological and mathematical models. In predator–prey models, dispersal will represent migration of either the prey population, the predator population, or both [1, 2]. There has been great interest in the study of mathematical models of populations with species dispersal among patches, such as a single population dispersal [5,6,7,8], and the dispersal of both prey and predator among patches [9,10,11]. It is challenging to add time delays to predator–prey models for the mathematical analysis. We shall investigate how the dispersal and dispersal delays interact to affect the stability of the predator–prey metapopulation model.
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