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Search Results (3)

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Keywords = Beddington–DeAngelis form

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8 pages, 578 KB  
Proceeding Paper
A Diseased Three-Species Harvesting Food Web Model with Various Response Functions
by Thangavel Megala, Thangaraj Nandha Gopal, Manickasundaram Siva Pradeep and Arunachalam Yasotha
Biol. Life Sci. Forum 2024, 30(1), 17; https://doi.org/10.3390/IOCAG2023-16876 - 11 Mar 2024
Cited by 2 | Viewed by 1008
Abstract
The purpose of this work is to present a three-species harvesting food web model that takes into account the interactions of susceptible prey, infected prey, and predator species. Prey species are assumed to expand logistically in the absence of predator species. The Crowley–Martin [...] Read more.
The purpose of this work is to present a three-species harvesting food web model that takes into account the interactions of susceptible prey, infected prey, and predator species. Prey species are assumed to expand logistically in the absence of predator species. The Crowley–Martin and Beddington–DeAngelis functional responses are used by predators to consume both susceptible and infected prey. Additionally, susceptible prey is consumed by infected prey in the formation of a Holling type II response. Both prey species are considered when prey harvesting is taken into account. Boundedness, positivity, and positive invariance are considered in this study. The investigation covers all the equilibrium points that are biologically feasible. Local stability is evaluated by analyzing the distribution of eigen values, while global stability is evaluated using suitable Lyapunov functions. Also, Hopf bifurcation is analyzed at the harvesting rate H1. At the end, we evaluate the numerical solutions based on our findings. Full article
(This article belongs to the Proceedings of The 2nd International Online Conference on Agriculture)
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8 pages, 944 KB  
Proceeding Paper
An Eco-Epidemiological Model Involving Prey Refuge and Prey Harvesting with Beddington–DeAngelis, Crowley–Martin and Holling Type II Functional Responses
by Megala Thangavel, Nandha Gopal Thangaraj, Siva Pradeep Manickasundaram and Yasotha Arunachalam
Eng. Proc. 2023, 56(1), 325; https://doi.org/10.3390/ASEC2023-15812 - 2 Nov 2023
Cited by 4 | Viewed by 927
Abstract
This paper represents a three-species food web model based on the connections between susceptible prey, infected prey, and predator species. It is considered that in the absence of predator species, prey species grow logistically. Predators consume susceptible and infected prey in the form [...] Read more.
This paper represents a three-species food web model based on the connections between susceptible prey, infected prey, and predator species. It is considered that in the absence of predator species, prey species grow logistically. Predators consume susceptible and infected prey in the form of Crowley–Martin and Beddington–DeAngelis functional responses. Also, infected prey consumes susceptible prey in the form of Holling type II interactions. Here, prey refuge and harvesting in prey with disease in a prey population are taken into consideration. Positiveness, boundedness, and positive invariance are examined. All biologically feasible equilibrium points are investigated. The local stability of positive equilibria and their global stability are analyzed by the suitable Lyapunov functions. Finally, numerical solutions are analyzed according to our findings. Full article
(This article belongs to the Proceedings of The 4th International Electronic Conference on Applied Sciences)
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20 pages, 506 KB  
Article
Qualitative Analysis in a Beddington–DeAngelis Type Predator–Prey Model with Two Time Delays
by Miao Peng, Rui Lin, Yue Chen, Zhengdi Zhang and Mostafa M. A. Khater
Symmetry 2022, 14(12), 2535; https://doi.org/10.3390/sym14122535 - 30 Nov 2022
Cited by 4 | Viewed by 2177
Abstract
In this paper, we investigate a delayed predator–prey model with a prey refuge where the predator population eats the prey according to the Beddington–DeAngelis type functional response. Firstly, we consider the existence of equilibrium points. By analyzing the corresponding characteristic equations, the local [...] Read more.
In this paper, we investigate a delayed predator–prey model with a prey refuge where the predator population eats the prey according to the Beddington–DeAngelis type functional response. Firstly, we consider the existence of equilibrium points. By analyzing the corresponding characteristic equations, the local stability of the trivial equilibrium, the predator–extinction balance, and the coexistence equilibrium of the system are discussed, and the existence of Hopf bifurcations concerning both delays at the coexistence equilibrium are established. Then, in accordance with the standard form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and stability of bifurcating period solutions are derived. Finally, representative numerical simulations are performed to validate the theoretical analysis. Full article
(This article belongs to the Special Issue Symmetries of Difference Equations, Special Functions and Orthogonal Polynomials)
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