Simple reaction-diffusion population model on scale-free networks.

We study a simple reaction-diffusion population model [proposed by A. Windus and H. J. Jensen, J. Phys. A: Math. Theor. 40, 2287 (2007)] on scale-free networks. In the case of fully random diffusion, the network topology cannot affect the critical death rate, whereas the heterogeneous connectivity can cause smaller steady population density and critical population density. In the case of modified diffusion, we obtain a larger critical death rate and steady population density, at the meanwhile, lower critical population density, which is good for the survival of species. The results were obtained using a mean-field-like framework and were confirmed by computer simulations.