Resistance noise in nonlinear resistor networks

Cohn’s theorem is extended to the case of circuit elements with the nonlinear I-V characteristic V=${\mathrm{rI}}^{\mathrm{\alpha }}$. This simplifies the study of resistance noise in nonlinear resistor networks. Exact exponent inequalities are derived. Fractal and percolating structures are considered. The infinite number of exponents necessary to characterize completely the electrical properties of linear and nonlinear percolating networks are calculated within the Migdal-Kadanoff approximation.