Abstract

<abstract> The global dynamics of the Nicholson's blowfly reaction-diffusion model with zero Dirichlet boundary condition is less understood. In this paper, we provide a discrete version of diffusive Nichlson's blowflies equation with zero Dirichlet boundary condition. Local and global stability of the equilibria are obtained by some comparison arguments, fluctuation method and the theory of exponential ordering. Hopf bifurcation at the positive equilibrium and the global existence of the periodic solutions are studied by local and global Hopf bifurcation theory. </abstract>

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