Stability and Hopf bifurcation of a heterogeneous diffusive model with spatial memory

The spatial memory and maturation time are incorporated into the spatially heterogeneous single advection-diffusion population model. The combined effects of memory, maturation and heterogeneity on the stability and the Hopf bifurcation of the model at the spatially nonconstant positive steady state are presented. It is found that the model could undergo the Hopf bifurcation under some conditions. However it only experiences a single stability switch from stability to instability with increases of delay, and the large diffusion could not lead to multiple stability switches of such model with the interaction of memory and maturation delays, as contrast to the case without spatial memory.