Linear and nonlinear regime of a Random Resistor Network under biased percolation

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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.