Abstract
We invest a predator‐prey model of Holling type‐IV functional response with stage structure and double delays due to maturation time for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and sufficient for the global stability of the equilibrium point of predator extinction are obtained. The most important outcome of this paper is that the variation of predator stage structure can affect the existence of the interior equilibrium point and drive the predator into extinction by changing the maturation (through‐stage) time delay. Our linear stability work and numerical results show that if the resource is dynamic, as in nature, there is a window in maturation time delay parameters that generate sustainable oscillatory dynamics.
Highlights
Predator-prey models are arguably the most fundamental building blocks of the any bioand ecosystems as all biomasses are grown out of their resource masses
We present a qualitative analysis for the predator-prey system 1.7 by incorporating stage structures for both prey and predator
The main goal of this paper is to study the combined effects of the stage structure on prey and predator on the dynamics of the system
Summary
Predator-prey models are arguably the most fundamental building blocks of the any bioand ecosystems as all biomasses are grown out of their resource masses. Their extinctions are often the results of their failure in obtaining the minimum level of resources needed for their subsistence Depending on their specific settings of applications, predator-prey models can take the forms of resource-consumer, plant-herbivore, parasite-host, tumor cells virus -immune system, susceptible-infectious interactions, and so forth. Motivated by the above important works 23–25 , in the present paper, we consider the following stage-structured predator-prey system with Holling type-IV functional response, which takes the form: dxj t dt bx − d1xj − be−d1τ1 x t − τ1 , dx t dt be−d1τ1 x t − τ1. The main goal of this paper is to study the combined effects of the stage structure on prey and predator on the dynamics of the system.
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