Unraveling the combined actions of a Holling type III predator–prey model incorporating Allee response and memory effects

Abstract

In this article, we have studied a memory dependent prey–predator model with logistic type prey growth subject to the Allee effect and Holling type‐III functional response. To include the memory effect, we have used here a fractional order system. The model contains at most four equilibrium points among which one is trivial, two are axial, and the last one is interior. Here we have studied behavior of these four equilibrium points using eigen analysis method. Our investigation shows that the trivial equilibrium point is stable for strong Allee effect, and unstable for weak Allee effect. Between the two axial equilibrium points, one is stable under certain condition but the other is always unstable. This unstable equilibrium point exists only for strong Allee case. The interior equilibrium point arises when the axial equilibrium point is unstable. Stability condition of this interior equilibrium point depends on the parametric relationship. The schematic diagram divides the a‐p plane into five sub‐regions in both the cases of memory dependent and memory less system. The number and nature of the equilibrium points in different sub‐regions are different. Finally, we have drawn the bifurcation diagrams considering all the equilibrium points in different sub‐regions and the results are concluded at the end.

Student Perceptions of, and Attitudes toward, Bats in Barak Valley, Assam, India

“…Despite the fact that numerous ecological models have been developed and have significantly aided our understanding of how prey and predator interactions operate within a system, numerous ecological systems are emerging that do not fall within the collection of mathematical transformations of prey-predator ecological systems. Starting with a simple one-prey, onepredator interaction environment, mathematical models are evolving to incorporate various ecological complexities such as the allee effect [3][4][5][6], fear effect [7][8][9], memory effect [6,9,10] and others, which exist even in ostensibly simple ecosystems and are a recent area of interest.…”

A Stochastic Framework for Solving the Prey-Predator Delay Differential Model of Holling Type-III

“…Such responses are typically considered when the predator efficiently finds an alternate source with a low prey density. There are many investigations that have been presented based on the Allee effects and Holling 3 rd type using the functional response [42]. The delayed mathematical model with the Holling 3 rd type using the functional response is provided as [43]:…”

A Fractional-Order Predator-Prey Model with Age Structure on Predator and Nonlinear Harvesting on Prey

“…Biological equilibria is basically the equilibrium point of model (7) which exists in R 3 + := (x, y, z) : x ≥ 0, y ≥ 0, z ≥ 0, (x, y, z) ∈ R 3 . Therefore, the following equations are needed to solve.…”

“…Some modifications based on the biological behaviors are integrated to construct a better model. For example, the predator-prey model involving the effect of fear [1][2][3][4], the impact of Allee to the existence of prey and predator [5][6][7][8], and the exploitation of biological resources by harvesting [9][10][11].…”