The habitat loss and fragmentation is almost the greatest threat to the survival of the wild giant panda. In this paper, we construct a mathematical model to consider the effect of diffusion on giant pandas that live in complex patchy environments. Our discussion includes the studying of a diffusive n-dimensional single species model, sufficient conditions are derived for the permanence and extinction of the giant panda species. Especially, we also discuss the situations of diffusion of giant pandas between two patches, and numerical simulations are presented to illustrate the results. Furthermore, we consider the existence, uniqueness, and global stability of the positive periodic solution of the n-dimensional single species model. The implications of these results are significant for giant panda conservation.
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