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In this paper, we consider a difiusive delayed predator- prey model with Beddington-DeAngelis type functional response under homogeneous Neumann boundary conditions, where the dis- crete time delay covers the period from the birth of immature preys to their maturity. We investigate the global existence of nonneg- ative solutions and the long-term behavior of the time-dependent solution of the model. x 0(t) = bxm(t) i dixi(t) i be idi? xm(t i ?); x 0(t) = be idi? xm(t i ?) i ax 2(t) i mxm(t)y(t) 1 + k1xm(t) + k2y(t) ; y 0 (t) = nmxm(t)y(t) 1 + k1xm(t) + k2y(t) i dy(t); where xm(µ) > 0 is continuous on i? • µ • 0 and xi(0), xm(0), y(0) > 0. Here xm and y represent mature prey and predator densi- ties, respectively, while xi is the immature prey density. All constants are positive, and b means the birth rate of the mature prey; di is a mor- tality rate of immature prey; n is the birth rate of predator; m is the

ON A DIFFUSIVE PREDATOR-PREY MODEL WITH STAGE STRUCTURE ON PREY