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We consider a two-dimensional random resistor network (RRN) in the presenceof two competing biased percolations consisting of the breaking and recoveringof elementary resistors. These two processes are driven by the joint effects ofan electrical bias and of the heat exchange with a thermal bath. The electricalbias is set up by applying a constant voltage or, alternatively, a constantcurrent. Monte Carlo simulations are performed to analyze the network evolutionin the full range of bias values. Depending on the bias strength, electricalfailure or steady state are achieved. Here we investigate the steady-state ofthe RRN focusing on the properties of the non-Ohmic regime. In constant voltageconditions, a scaling relation is found between $<R>/<R>_0$ and $V/V_0$, where$<R>$ is the average network resistance, $<R>_0$ the linear regime resistanceand $V_0$ the threshold value for the onset of nonlinearity. A similar relationis found in constant current conditions. The relative variance of resistancefluctuations also exhibits a strong nonlinearity whose properties areinvestigated. The power spectral density of resistance fluctuations presents aLorentzian spectrum and the amplitude of fluctuations shows a significantnon-Gaussian behavior in the pre-breakdown region. These results compare wellwith electrical breakdown measurements in thin films of composites and of otherconducting materials.Comment: 15 figures, 23 page

Resistance and resistance fluctuations in random resistor networks under biased percolation