Extremal Dynamics Model on Evolving Networks

We investigate an extremal dynamics model of evolution with variable number of units. Because of addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly concentrated in the largest cluster. The time dependence of the number of units exhibits intermittent structure. The self-organized criticality is manifested by a power-law distribution of forward avalanches, but two regimes with distinct exponents $\tau =1.98\mathrm{}\pm 0.04$ and ${\tau }^{\prime }=1.65\mathrm{}\pm 0.05$ are found. The distribution of extinction sizes obeys a power law with exponent $2.32\pm 0.05$.