Bifurcation analysis in a predator-prey system with a functional response increasing in both predator and prey densities
- Authors
- Ryu, Kimun; Ko, Wonlyul; Haque, Mainul
- Issue Date
- 11월-2018
- Publisher
- SPRINGER
- Keywords
- Predator-prey; Bistability; Allee effect; Saddle-node; Bogdanov-Takens; Hopf bifurcation
- Citation
- NONLINEAR DYNAMICS, v.94, no.3, pp.1639 - 1656
- Indexed
- SCIE
SCOPUS
- Journal Title
- NONLINEAR DYNAMICS
- Volume
- 94
- Number
- 3
- Start Page
- 1639
- End Page
- 1656
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/131742
- DOI
- 10.1007/s11071-018-4446-0
- ISSN
- 0924-090X
- Abstract
- This paper presents a qualitative study of a predator-prey interaction system with the functional response proposed by Cosner et al. (Theor Popul Biol 56:65-75, 1999). The response describes a behavioral mechanism which a group of predators foraging in linear formation searches, contacts and then hunts a school of prey. On account of the response, strong Allee effects are induced in predators. In the system, we determine the existence of all feasible nonnegative equilibria; further, we investigate the stabilities and types of the equilibria. We observe the bistability and paradoxical phenomena induced by the behavior of a parameter. Moreover, we mathematically prove that the saddle-node, Hopf and Bogdanov-Takens types of bifurcations can take place at some positive equilibrium. We also provide numerical simulations to support the obtained results.
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