  We investigate the steady state of a two-dimensional random resistor network
subjected to two competing biased percolations as a function of the bias
strength. The properties of the linear and nonlinear regimes are studied by
means of Monte Carlo simulations. In constant current conditions, a scaling
relation is found between $<R>/<R>_0$ and $I/I_0$, where $<R>$ is the average
network resistance, $<R>_0$ the Ohmic resistance and $I_0$ an appropriate
threshold value for the onset of nonlinearity. A similar scaling relation is
found also for the relative variance of resistance fluctuations. These results
are in good agreement with electrical breakdown measurements performed in
composite materials.
