Constrained invasion percolation model: Growth via Leath bursts and the origin of seismic b-value

We analyze a new model for growing networks, the constrained Leath invasion percolation model. Cluster dynamics are characterized by bursts in space and time. The model quantitatively reproduces the observed frequency-magnitude scaling of earthquakes in the limit that the occupation probability approaches the critical bond percolation probability in d 1⁄4 2. The model may have application to other systems characterized by burst dynamics.