Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

Shaikh, Absos Ali; Das, Harekrishna; Ali, Nida

doi:10.1007/s40808-018-0441-1

Cited by 6 publications

(6 citation statements)

References 19 publications

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“…Equilibria and their stability criteria. In this section, we shall investigate the local stability analysis around equilibrium points of the system (6). The local stability analysis gives an idea to better understand the qualitative behavior of the system (6).…”

Section: Preliminariesmentioning

confidence: 99%

“…Proposition 3.1. The local stability conditions around the equilibrium points of the system (6) are listed in table 1.…”

Section: Preliminariesmentioning

confidence: 99%

“…In mathematical ecology, a simple common type of Holling functional responses were used in most of the models [2][3][4][5][6]. Recently, some researchers like Sahoo and Poria have investigated predator-prey models with general Holling-type interactions instead of commonly used Holling-type response functions [7,8].…”

Section: Introduction and Model Formulationmentioning

confidence: 99%

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Dynamics of an epidemic system with prey herd behavior and alternative resource to predator

Samanta¹,

Sahoo²,

Das³

2019

J. Phys. A: Math. Theor.

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A heterogeneous predator–prey system with herd behavior of prey is proposed. The predator individuals are affected by a disease. The predator is provided with alternative resources for long time survival. The objective of this study is to study the role of the alternative resource for controlling disease in a heterogeneous system. The dynamical behavior of the system is investigated throughout the theoretical studies and the results are verified using numerical simulations. The system is locally, as well as globally, stable under certain conditions. Also, the system undergoes Hopf bifurcation at a critical level of infection. The obtained results show that a disease-free system can be achieved by supplying a suitable alternative resource. The present study in an epidemic system introduces a new platform for controlling disease.

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Section: Preliminariesmentioning

confidence: 99%

“…Proposition 3.1. The local stability conditions around the equilibrium points of the system (6) are listed in table 1.…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of an epidemic system with prey herd behavior and alternative resource to predator

Samanta¹,

Sahoo²,

Das³

2019

J. Phys. A: Math. Theor.

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“…The predation function of predators on prey in this model is linear or called Holling type I. Other common functional responses for predator-prey models are types II, III, and IV [4] [5] [6] [7]. Leslie and Gower modified the model by adding carrying capacity for the predator population in proportion to the size or number of the prey population [8].…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey

Putra

Himayati

2022

InPrime:Ind.Jour.Pure.Applied.Math

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We studied the Leslie-Gower model of predator-prey with herd behavior. The square root functional response models predator and prey interactions that show herd behavior. This study aims to determine the formulation of the predator-prey model with herd behavior on prey, knowing the fixed points and its stability and simulating the model numerically. We found three fixed points that may exist: the extinction point of both species, the extinction of predator point, and the point of coexistence of the two species. The extinction of predator points is always unstable, while the point of coexistence of the two species can be stable under certain conditions. Due to the presence of square roots, the behavior of the solutions near the extinction point of the two species is not readily apparent. Numeric simulation shows that changing the initial condition and parameters can change the system's stability.Keywords: predator-prey; functional response; herd behavior; square root functional response, Leslie-Gower model. AbstrakArtikel membahas model predator prey Leslie-Gower dengan perilaku bergerombol pada prey. Interaksi predator dan prey yang menunjukkan perilaku bergerombol dimodelkan dengan fungsi respon akar kuadrat. Penelitian ini bertujuan untuk mengetahui formulasi model predator-prey dengan perilaku bergerombol pada prey, mengetahui titik ekuilibrium dan kestabilannya serta menyimulasikan model tersebut secara numerik. Hasil menunjukkan terdapat tiga titik tetap yang mungkin eksis, yaitu titik kepunahan kedua spesies, titik kepunahan predator dan titik koeksistensi kedua spesies. Titik kepunahan predator selalu tidak stabil, sedangkan titik koeksistensi kedua spesies bisa stabil dengan syarat tertentu. Karena adanya akar kuadrat, perilaku solusi di dekat titik kepunahan kedua spesies tidak mudah terlihat. Simulasi numerik menunjukkan bahwa perubahan nilai awal dan parameter dapat mengubah kestabilan sistem.Kata Kunci: predator prey; fungsi respons; perilaku bergerombol; fungsi respon akar kuadrat; model Leslie-Gower.

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“…If the predator is more active hunting when prey density is getting large and less active when prey density decreases, then the Holling type III form can fit better [10]. The Leslie-Gower model and Holling type III has been investigated by several authors as in [6] [11].…”

Section: Introductionmentioning

confidence: 99%

Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III

Firdiansyah¹

2021

Jambura J. Math

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In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases. In the end, several numerical solutions are presented to check the analytical results.

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Study of a predator–prey model with modified Leslie–Gower and Holling type III schemes

Cited by 6 publications

References 19 publications

Dynamics of an epidemic system with prey herd behavior and alternative resource to predator

Dynamics of an epidemic system with prey herd behavior and alternative resource to predator

Stability Analysis of Leslie-Gower Model with Herd Behavior on Prey

Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III

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