We consider a two-dimensional random resistor network (RRN) in the presence
of two competing biased percolations consisting of the breaking and recovering
of elementary resistors. These two processes are driven by the joint effects of
an electrical bias and of the heat exchange with a thermal bath. The electrical
bias is set up by applying a constant voltage or, alternatively, a constant
current. Monte Carlo simulations are performed to analyze the network evolution
in the full range of bias values. Depending on the bias strength, electrical
failure or steady state are achieved. Here we investigate the steady-state of
the RRN focusing on the properties of the non-Ohmic regime. In constant voltage
conditions, a scaling relation is found between /0 and V/V0, where
is the average network resistance, 0 the linear regime resistance
and V0 the threshold value for the onset of nonlinearity. A similar relation
is found in constant current conditions. The relative variance of resistance
fluctuations also exhibits a strong nonlinearity whose properties are
investigated. The power spectral density of resistance fluctuations presents a
Lorentzian spectrum and the amplitude of fluctuations shows a significant
non-Gaussian behavior in the pre-breakdown region. These results compare well
with electrical breakdown measurements in thin films of composites and of other
conducting materials.Comment: 15 figures, 23 page