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Please use this identifier to cite or link to this item: http://dspace.bits-pilani.ac.in:8080/jspui/xmlui/handle/123456789/10989
Title: Modeling the Effect of Fear in a Prey–Predator System with Prey Refuge and Gestation Delay
Authors: Dubey, Balram
Keywords: Mathematics
Fear Effect
Prey refuge
Hopf-bifurcation
Gestation delay
Lyapunov exponent
Issue Date: 2019
Publisher: World Scientific
Abstract: Recently, some field experiments and studies show that predators affect prey not only by direct killing, they induce fear in prey which reduces the reproduction rate of prey species. Considering this fact, we propose a mathematical model to study the fear effect and prey refuge in prey–predator system with gestation time delay. It is assumed that prey population grows logistically in the absence of predators and the interaction between prey and predator is followed by Crowley–Martin type functional response. We obtained the equilibrium points and studied the local and global asymptotic behaviors of nondelayed system around them. It is observed from our analysis that the fear effect in the prey induces Hopf-bifurcation in the system. It is concluded that the refuge of prey population under a threshold level is lucrative for both the species. Further, we incorporate gestation delay of the predator population in the model. Local and global asymptotic stabilities for delayed model are carried out. The existence of stable limit cycle via Hopf-bifurcation with respect to delay parameter is established. Chaotic oscillations are also observed and confirmed by drawing the bifurcation diagram and evaluating maximum Lyapunov exponent for large values of delay parameter.
URI: https://www.worldscientific.com/doi/10.1142/S0218127419501955
http://dspace.bits-pilani.ac.in:8080/xmlui/handle/123456789/10989
Appears in Collections:Department of Mathematics

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