Linear and nonlinear regime of a random resistor network under biased percolation

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/I0, where 〈R〉 is the average network resistance, 〈R〉0 the Ohmic resistance and I0 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.