Dynamics of adding variable prey refuge and an Allee effect to a predator–prey model

Molla, Hafizul; Sarwardi, Sahabuddin; Smith, Stacey R.; Haque, Mainul

doi:10.1016/j.aej.2021.09.039

Cited by 31 publications

(7 citation statements)

References 27 publications

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“…Typically, there are two main types of prey refuges in predator-prey models. One type considers the prey refuge as a constant number [12,13], while the other type assumes that the refuge is proportional to the size of the prey population [14][15][16][17]. Therefore, if xr denotes the prey refuge, model (1.1) is modified as…”

Section: Introductionmentioning

confidence: 99%

The Impact of Predator-dependent Prey Refuge on the Dynamics of a Leslie-Gower Predator-prey Model

Yang,

Chen

2023

ARJOM

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In this paper, we propose a new Leslie-Gower predator-prey model with predator-dependent prey refuge. Firstly, we obtain the positivity and boundedness of the system solution. Secondly, we prove that the origin is unstable using blow-up method, analyze the existence and local stability of the boundary equilibrium point and positive equilibrium point, and prove that the unique positive equilibrium point of the system is globally asymptotically stable by constructing a suitable Dulac function. Finally, mathematic analysis and numerical simulation show that: (1) when the strength of the predator-dependent prey refuge k = 0 , the dynamics of the predator-prey system without predator-dependent prey refuge are consistent with the results obtained from the traditional Leslie-Gower predator-prey system; (2) when k tends to positive infinity, the predator-dependent refuge lead to prey population densities fall somewhere between without prey refuge and with proportional refuge. However, the predator densities within this new form of the predator-dependent prey refuge is greater than the densities of predators without prey refuge and with proportional refuge; (3) increasing the strength k of the predator-dependent prey refuge can increase the densities of predator and prey populations respectively.

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Section: Introductionmentioning

confidence: 99%

The Impact of Predator-dependent Prey Refuge on the Dynamics of a Leslie-Gower Predator-prey Model

Yang,

Chen

2023

ARJOM

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“…Difference equations or other forms, such as discrete-time map-pings, are used to represent their interactions. The dynamical behaviour of a discrete-time prey-predator model is typically more sophisticated than that of the equivalent continuous-time models [6][7][8][9] . Different mathematical tools were used for the considerations of the predator prey models.…”

Section: Introduction Of the Modelmentioning

confidence: 99%

Habitat complexity of a discrete predator-prey model with Hassell-Varley type functional response

Kundu,

Alzabut,

E.Samei

et al. 2023

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Prey-predator models with a refuge eﬀect are particularly signiﬁcant in ecology. The two common conceptions of refuge in the literature are continual refuge and refuge pro-portionate to prey. Academics are already paying attention to new types of refuge concepts. Prey-predator interaction has become a prominent issue in recent biomathe-matical studies due to its environmental inﬂuence. In this paper, the habitat complexity of a predator-prey model with Hassell-Varley type functional response is considered. For this, we focused our study on the question of existence and uniqueness in Sec. 2. And Sec. 3 is devoted to show a generalized stability. Note that this representation also al-lows us to generalize the results obtained recently in the literature. In Sec. 4, we have studied the numerical algorithm for the suggested problem. The paper is ended by two examples illustrating our results.

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“…The existence of these interactions will maintain the balance, stability, and productivity of an ecosystem. One form of interaction in an ecosystem is predation, which is the interaction between prey and predator [1]. One of the goals of this interaction is to stabilize the number of prey and predator populations in an ecosystem.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of Three Species Food Chain With Intraspecific Competition and Harvesting on Predator

Manaqib

Suma'inna

Zahra

2022

BAREKENG: J. Il. Mat. & Ter.

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This research develops a mathematical model of three species of food chains between prey, predator, and top predator by adding intraspecific competition and harvesting factors. Interaction between prey with predator and interaction between predator with top predator uses the functional response type II. Model formation begins with creating a diagram food chain of three species compartments. Then a nonlinear differential equation system is formed based on the compartment diagram. Based on this system four equilibrium points are obtained. Analysis of local stability at the equilibrium points by linearization shows that there is one unstable equilibrium point and three asymptotic stable local equilibrium points. Numerical simulations at equilibrium points show the same results as the results of the analysis. Then numerical simulations on several parameter variations show that intraspecific competition has little effect on population changes in predator and top predator. While the harvesting parameter predator affects the population of predator and top predator.

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Dynamics of adding variable prey refuge and an Allee effect to a predator–prey model

Cited by 31 publications

References 27 publications

The Impact of Predator-dependent Prey Refuge on the Dynamics of a Leslie-Gower Predator-prey Model

The Impact of Predator-dependent Prey Refuge on the Dynamics of a Leslie-Gower Predator-prey Model

Habitat complexity of a discrete predator-prey model with Hassell-Varley type functional response

Mathematical Model of Three Species Food Chain With Intraspecific Competition and Harvesting on Predator

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