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In this work we study the localization properties of diluted and nondiluted disordered direct transmission lines (TLs), when we distribute two values of inductances, L A and L B , according to an asymmetric dichotomous sequence. Using the scaling properties of the participation number D we study the localization properties in the thermodynamic limit. For certain and parameter speci¯c values, which characterize the dichotomous noise, we have found the following limit conditions: lim !1 mð!; ; Þ ! 1:0 or lim !1 mð!; ; Þ ! 1:0, for the appearing of the disorder-order transitions. Here mð!; ; Þ are the slopes of the linear relationships between lnðDÞ and lnðNÞ. In addition, in each ! c resonance frequency generated by the dilution process we demonstrate the existence of extended intermediate states in the thermodynamic limit.

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In this article we report exact analytical and numerical evidences of the occurrence of the stochastic resonance phenomenon in simple electrical circuits driven by a quadratic Gaussian colored noise and by a Gaussian white noise. As an example we have used an RL configuration. However, it is clear that the phenomenon occurs in any other configuration governed by the same type of evolution equation. The main result is that the phenomenon occurs with a quadratic colored noise. When noise enters only linearly we have verified that the stochastic resonance occurs both with colored noise and white noise. The robustness of our results were verified by calculating the variance as a function of time in each case. We believe that the results obtained could be observed in a laboratory experiment using some kind of digital resistance. The white noise limit with quadratic noise was excluded.Index Terms-Stochastic resonance phenomenon, simple electrical circuits, Gaussian colored noise, Gaussian white noise.