Stationary regime of random resistor networks under biased percolation

The state of a two-dimensional random resistor network, resulting from the simultaneous evolutions of two competing biased percolations, is studied in a wide range of bias values. Monte Carlo simulations show that when the external current 1 is below the threshold value for electrical breakdown, the network reaches a steady state with nonlinear current-voltage characteristics. The properties of this nonlinear regime are investigated as a function of different model parameters. A scaling relation is found between (R)/(R)(0) and I/I-0, where (R) is the average resistance, (R)(0) the linear regime resistance and to the threshold value for the onset of nonlinearity. The scaling exponent is found to be independent of the model parameters. A similar scaling behaviour is also found for the relative variance of resistance fluctuations. These results compare well with resistance measurements in composite materials performed in the Joule regime up to breakdown.