Article ID Journal Published Year Pages File Type
470499 Computers & Mathematics with Applications 2013 15 Pages PDF
Abstract

In this paper, we consider the direction and stability of time-delay induced Hopf bifurcation in a three species food-chain model with diffusion. By means of analyzing eigenvalue spectrum and Lyapunov functional, we show that the positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold. Using the norm form and the center manifold theory, we investigate the stability and direction of the Hopf bifurcation. The instability of the Hopf bifurcation leads to the emergence of spatial patterns. Numerical calculations are performed to illustrate our theoretical results.

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Physical Sciences and Engineering Computer Science Computer Science (General)
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