  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.
