Stability analysis of coexistence of three species prey–predator model

In this paper, we have proposed a prey–predator model for the study of dynamical behaviors of three species such as toxin-producing Phytoplankton, Zooplankton and Fish in a fishery system. The stability condition, existence condition of equilibrium and bifurcation have also been established. In this...

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Bibliographic Details
Published in:Nonlinear dynamics 2015-07, Vol.81 (1-2), p.373-382
Main Authors: Panja, Prabir, Mondal, Shyamal Kumar
Format: Article
Language:English
Subjects:
Automotive Engineering
Bifurcations
Classical Mechanics
Control
Dynamical Systems
Engineering
Fisheries
Mechanical Engineering
Original Paper
Phytoplankton
Response functions
Stability analysis
Vibration
Zooplankton
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Summary:In this paper, we have proposed a prey–predator model for the study of dynamical behaviors of three species such as toxin-producing Phytoplankton, Zooplankton and Fish in a fishery system. The stability condition, existence condition of equilibrium and bifurcation have also been established. In this paper, Holling type II functional response function has been considered to analysis of the proposed model. All equilibriums of the proposed system are determined, and the behavior of the system is also investigated near the positive equilibrium point. At the end, local stability of the system is analyzed by numerical illustrations.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-015-1997-1