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Global stability and bifurcation of time delayed prey-predator system incorporating prey refuge

Jana, S and Chakraborty, M and Chakraborty, K and Kar, TK (2012) Global stability and bifurcation of time delayed prey-predator system incorporating prey refuge. Mathematics and Computers in Simulation, 85. pp. 57-77.

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Abstract

This paper describes a prey-predator model with Holling type II functional response incorporating prey refuge. The equilibria of the proposed system are determined and the behavior of the system is investigated around equilibria. Density-dependent mortality rate for the predator is considered as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the co-existing equilibrium point. Discrete-type gestational delay of predators is also incorporated on the system. The dynamics of the delay induced prey-predator system is analyzed. Delay preserving stability and direction of the system is studied. Global stability of the delay preserving system is shown. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations.

Item Type: Article
Additional Information: Copyright of this article belongs to Elsevier.
Uncontrolled Keywords: Prey–predator;Refuge;Delay;Hopf bifurcation;Global stability
Subjects: Oceanography > oceanography
Depositing User: INCOIS Library
Date Deposited: 13 Dec 2013 06:40
Last Modified: 13 Dec 2013 06:40
URI: http://moeseprints.incois.gov.in/id/eprint/135

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