  With a simple attack and repair evolution model, we investigate and compare
the stability of the Erdos-Renyi random graphs (RG) and Barabasi-Albert
scale-free (SF) networks. We introduce a new quantity, invulnerability I(s), to
describe the stability of the system. We find that both RG and SF networks can
evolve to a stationary state. The stationary value Ic has a power-law
dependence on the average degree <k>_rg for RG networks; and an exponential
relationship with the repair probability p_sf for SF networks. We also discuss
the topological changes of RG and SF networks between the initial and
stationary states. We observe that the networks in the stationary state have
smaller average degree <k> but larger clustering coefficient C and stronger
assortativity r.
