Prey predator model with Beddington-DeAngelis functional response
Authors: 
Dongyang Wang, Yang GaoAuthors Info & Claims
Dongyang Wang, Yang GaoAuthors Info & ClaimsPages 127 - 131
Abstract
In this study, the prey predator model with different genotypes are discussed, Considering the interference within the predator population during the predation process, the Beddington-DeAngelies type functional response function was added to the model. Firstly, the positive and boundedness of the understanding are proved, Subsequently, the model is modified to include a prey with a single genotype and a predator with a single genotype in order to analyze its equilibrium point and stability. Then the Routh Hurwitz criterion is employed to demonstrate the local stability of the model, while the Lyapunov function is formulated to establish its global asymptotic stability. Finally, numerical simulation is used to verify the results. It also demonstrated that moderate interference among predators can regulate the population of prey.
References
[1]
Huisen Zhang, Yongli Cai, Shengmao Fu and Weiming Wang. 2019. Impact of the fear effect in a prey-predator model incorporating a prey refuge. Applied Mathematics and Computation. (September 2019), 328-337.
[2]
Bushra E. Kashem and Hassan F. Al Husseiny. 2024. The dynamic of two prey–One predator food web model with fear and harvesting. Partial Differential Equations in Applied Mathematics. (September 2024), 100875-100875.
[3]
Pal, D, Kesh, D. and Mukherjee, D. 2023. Qualitative study of cross-diffusion and pattern formation in leslie–gower predator–prey model with fear and allee effects. Chaos, Solitons & Fractals, 167 (February 2023), 113033.
[4]
Sivasamy Ramasamy, David Banjerdpongchai and PooGyeon Park. 2025. Stability and Hopf-bifurcation analysis of diffusive Leslie–Gower prey–predator model with the Allee effect and carry-over effects. Mathematics and Computers in Simulation. (January 2025), 19-40.
[5]
Savitri, D, Suryanto, A, Kusumawinahyu, W. M. and Abadi. 2020. Dynamics of two preys – one predator system with competition between preys. Journal of Physics: Conference Series. (June 2020), 4-5.
[6]
Armisén David, Refki Peter Nagui, Crumière Antonin Jean Johan, Viala Séverine, Toubiana William and Khila Abderrahman. 2015. Predator strike shapes antipredator phenotype through new genetic interactions in water striders. Nature communications. (September 2015), 8153.
[7]
Mi, Y. Y, Song, C. and Wang, Z. C. 2023. Global existence of a diffusive predator-prey model with prey-stage structure and prey-taxis. ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees. (April 2023), 90.
[8]
Li, J, Li, L, and Zhao, S. 2023. Predator-prey survival pressure is sufficient to evolve swarming behaviors. new journal of physics. (August 2023).
[9]
Zhang, Y. and Huang, J. 2022. Bifurcation analysis of a predator–prey model with Beddington–DeAngelis functional response and predator competition. Mathematical Methods in the Applied Sciences. 45, (May 2022), 9894 - 9927.
[10]
Shi, L, Wang, L, and Zhu, X. W. P. 2022 Dynamics of an infection-age HIV diffusive model with latent infected cell and Beddington-DeAngelis infection incidence. European Physical Journal Plus. 137(2), (February 2022), 212.
[11]
Liu S Q and Beretta E. 2006. A stage-structured predator-prey model of. Siam Journal on Applied Mathematics.66(4) (January 2006), 1101-1129.
[12]
Santhosh Kumar G, Gunasundari C, Boulaaras, S. M and Aakash M. Genetic differentiation of prey predator interaction model along with an Holling type-II functional response. Partial Differential Equations in Applied Mathematics. (March 2024), 100649.
[13]
Liu, L, Wong, Y. S, and Lee, B. H. K. 2000. Application of the centre manifold theory in non-linear aeroelasticity. Journal of Sound & Vibration, 234(4). (July 2000), 641-659.
[14]
Amarathunga Don Chathurika, Parry Hazel, Grundy John and Dorin Alan. (2024). A predator–prey population dynamics simulation for biological control of Frankliniella occidentalis (Western Flower Thrips) by Orius laevigatus in strawberry plants. Biological Control. (January 2024), 105409.
[15]
Chen Miqin and Yang Wensheng. 2023. Complex dynamics of a Leslie–Gower predator–prey model with Allee effect and variable prey refuge. International Journal of Dynamics and Control (6), (May 2023), 2831-2841.
Index Terms
- Prey predator model with Beddington-DeAngelis functional response
Recommendations
Study on a non-autonomous predator-prey system with Beddington-DeAngelis functional response
In this paper, a predator-prey system with Beddington-DeAngelis functional response is studied, where the predator preys on n competing preys. We prove that the system admits very rich dynamics, including permanence, ultimate boundedness, extinction. ...
Periodic solutions of a discrete-time nonautonomous predator-prey system with the Beddington-Deangelis functional response
In this paper, we investigate a discrete-time nonautonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable ...
Permanence of the Impulsive Predator-Prey System with Beddington-DeAngelis Functional Response
ICIC '09: Proceedings of the 2009 Second International Conference on Information and Computing Science - Volume 04Beddington-DeAngelis functional response predator-prey system , which may inherently oscillate, is considered by introducing periodic constant impulsive immigration of predator. The Local stability of the prey extinction periodic solution, as well as ...
Comments
Information & Contributors
Information
Published In
November 2024
208 pages
ISBN:9798400711657
DOI:10.1145/3708360
Copyright © 2024 Copyright held by the owner/author(s). Publication rights licensed to ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 13 January 2025
Check for updates
Author Tags
Qualifiers
- Research-article
Conference
ICMML 2024
ICMML 2024: 2024 International Conference on Mathematics and Machine Learning
November 8 - 10, 2024
Nanjing, China
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 19Total Downloads
- Downloads (Last 12 months)19
- Downloads (Last 6 weeks)11
Reflects downloads up to 07 Mar 2025
Other Metrics
Citations
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in