Author: Li Xin Jiang Weihua Shi Junping
Publisher: Oxford University Press
ISSN: 1464-3634
Source: IMA Journal of Applied Mathematics, Vol.78, Iss.2, 2013-04, pp. : 287-306
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Abstract
The reactiondiffusion HollingTanner predatorprey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partial differential equation (PDE), we consider the Turing instability of the equilibrium solutions and the bifurcating periodic solutions. Through both theoretical analysis and numerical simulations, we show the bistability of a stable equilibrium solution and a stable periodic solution for ordinary differential equation and the phenomenon that a periodic solution becomes Turing unstable for PDE.
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