The stability and Hopf bifurcation of the diffusive Nicholson’s blowflies model in spatially heterogeneous environment

In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when diffusion rate is large. We show that ratio of average maximum per capita egg production to death affects dynamics model. The unique positive steady state locally asymptotically stable if less than a critical value. However, greater value, large time delay can make unstable through Hopf bifurcation. Especially, first bifurcation value tends ''average'' DDE infinity. Moreover, direction forward, and bifurcating periodic solution from orbitally stable, which improves earlier result by Wei Li (Nonlinear. Anal., 60: 1351-1367, 2005).