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A Condition for Hopf bifurcation to occur in Equations of Lotka-Volterra Type with Delays

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Author(s): Chol Kim

Journal: Journal of Theoretical Physics and Cryptography
ISSN 2322-3138

Volume: 4;
Start page: 13;
Date: 2013;
Original page

Keywords: Lotka-Volterra equation | distributed delay | Hopf bifurcation | stability | equilibrium

ABSTRACT
It is known that Lotka-Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested one predator – two prey model. Using the expectation of the distribution of the delay as a bifurcation parameter, we show that the equilibrium that was asymptotic stable becomes unstable and Hopf bifurcation can occur as the expectation crosses some critical values.
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