Comparative studies on a predator–prey model subjected to fear and Allee effect with type I and type II foraging

Halder, Susmita; Bhattacharyya, Joydeb; Pal, Samares

doi:10.1007/s12190-019-01275-w

Cited by 15 publications

(7 citation statements)

References 20 publications

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“…Furthermore, they have also showed that the harvesting amount must adjust to the growth rate and the Allee coefficient. In [53], a predator–prey model has been considered where the growth rate of the prey is affected by both the Allee and fear effects with two different foraging behaviors of the predator. The total sizes of both prey and predator populations decreased due to the gradual increase of fear levels.…”

Section: Introductionmentioning

confidence: 99%

On the slow–fast dynamics of a tri‐trophic food chain model with fear and Allee effects

Salman,

Shchepakina

2024

Math Methods in App Sciences

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A three‐species food chain model with Allee and fear effects on both prey and predator is investigated in this work. The model consists of ODEs describing the evolution and interaction of prey, predator, and top predator populations in a biological system. We assume that the intrinsic growth rate of the prey is much smaller than a threshold value determined by other biological parameters of the model. Consequently, the model is transformed into a singularly perturbed system that acts on two different time scales, ranging from slow for both prey and predator to fast for the top predator. Positivity and boundedness of the solutions of the model along with the stability for its equilibria are investigated. The model possesses the exact invariant manifold with changing stability (black swan) and exhibits the canard phenomenon. Some numerical simulations are performed to validate our analysis.

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Section: Introductionmentioning

confidence: 99%

On the slow–fast dynamics of a tri‐trophic food chain model with fear and Allee effects

Salman,

Shchepakina

2024

Math Methods in App Sciences

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“…Teng et al [12] investigated a fractional-order predator-prey model incorporating a prey refuge, proved the existence, uniqueness, non-negativity and boundedness of the solutions for the model, analyzed the existence of various equilibrium, and obtained some sufficient conditions for the global asymptotic stability of predator-extinction equilibrium and coexistence equilibrium. In addition, scholars have found other influences such as fear effect, harvest effect, toxins and seasonality in the study of predator-prey models, for example, [13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Codimension-two bifurcations analysis of a discrete predator-prey model incorporating a prey refuge

Rui

Chen

2023

Preprint

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“…A density-dependent prey-predator model having the effect of harvesting is investigated in [ 34 ]. Moreover, prey-predator population model with fear and Allee effects is considered in [ 35 ]. This paper investigates the global existence of the solution of a diffusive directed dynamic (DDD) model, which is a variant of the classical RDE model.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal solutions of a diffusive directed dynamics model with harvesting

Kamrujjaman

Keya

Bulut

et al. 2022

J. Appl. Math. Comput.

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The study considers a directed dynamics reaction-diffusion competition model to study the density of evolution for a single species population with harvesting effect in a heterogeneous environment, where all functions are spatially distributed in time series. The dispersal dynamics describe the growth of the species, which is distributed according to the resource function with no-flux boundary conditions. The analysis investigates the existence, positivity, persistence, and stability of solutions for both time-periodic and spatial functions. The carrying capacity and the distribution function are either arbitrary or proportional. It is observed that if harvesting exceeds the growth rate, then eventually, the population drops down to extinction. Several numerical examples are considered to support the theoretical results. Supplementary Information The online version contains supplementary material available at 10.1007/s12190-022-01742-x.

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Comparative studies on a predator–prey model subjected to fear and Allee effect with type I and type II foraging

Cited by 15 publications

References 20 publications

On the slow–fast dynamics of a tri‐trophic food chain model with fear and Allee effects

On the slow–fast dynamics of a tri‐trophic food chain model with fear and Allee effects

Codimension-two bifurcations analysis of a discrete predator-prey model incorporating a prey refuge

Spatio-temporal solutions of a diffusive directed dynamics model with harvesting

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