Dynamical Analysis of a Beddington–DeAngelis Interacting Species System with Prey Harvesting
Joint Authors
Kim, Kyoung-Hwan
Guin, Lakshmi Narayan
Murmu, Reeta
Baek, Hunki
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-10-28
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
A reaction–diffusion interacting species system with Beddington–DeAngelis functional response that has been proposed in the environment of mathematical ecology, which provides the rise to spatial pattern formation, is investigated and associated with the models of deterministic dynamics.
The dynamical behaviour of a generalist predator–prey system with linear harvesting of each species and predator-dependent functional response is fully analyzed.
Conditions of stability behaviour of the interior equilibrium point are established properly.
Furthermore, we have recognized that the unique positive equilibrium point of the system is globally stable via appropriate Lyapunov function structure, which signifies that appropriate harvesting has no impact on the persistence property of the harvesting system.
Also, we establish the conditions for the existence of bifurcation phenomena including a saddle-node bifurcation and a Hopf bifurcation.
Subsequently, complete analysis regarding the impact of harvesting is carried out, and an interesting decision is that under some appropriate constraints, harvesting has immense impact on the final size of the interacting species.
In addition, in accordance with Turing’s ideas on morphogenesis , our analysis shows that harvesting effort in a reaction–diffusion predator–prey system plays a vital function for geological conservation of interacting species.
Finally, we discuss sufficient conditions for the existence of bionomic equilibrium point and the optimal harvesting policy attained by using the Pontryagin maximal principle.
American Psychological Association (APA)
Guin, Lakshmi Narayan& Murmu, Reeta& Baek, Hunki& Kim, Kyoung-Hwan. 2020. Dynamical Analysis of a Beddington–DeAngelis Interacting Species System with Prey Harvesting. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-22.
https://search.emarefa.net/detail/BIM-1200624
Modern Language Association (MLA)
Guin, Lakshmi Narayan…[et al.]. Dynamical Analysis of a Beddington–DeAngelis Interacting Species System with Prey Harvesting. Mathematical Problems in Engineering No. 2020 (2020), pp.1-22.
https://search.emarefa.net/detail/BIM-1200624
American Medical Association (AMA)
Guin, Lakshmi Narayan& Murmu, Reeta& Baek, Hunki& Kim, Kyoung-Hwan. Dynamical Analysis of a Beddington–DeAngelis Interacting Species System with Prey Harvesting. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-22.
https://search.emarefa.net/detail/BIM-1200624
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1200624