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Exact solutions to stochastic resonance systems and nonlinear stochastic circuits

There exist a common belief that random sequences are produced from very complicated phenomena, making impossible the construction of accurate mathematical models. It has been recently shown that under specific conditions the exact solutions to some chaotic functions can be generalized to produce truly random sequences. This establishes a transition from chaos to stochastic dynamics. Using this result we can obtain explicit output expressions for stochastic dynamics problems like those posed by stochastic resonant nonlinear systems. We show that in this kind of systems the phenomenon of noise-induced disorder-order can be more efficiently described with an information-theory approach through the determination of a parameter that measures the complexity of the dynamics. The Stochastic Resonance (SR) is just an example of the principal phenomenon wherein the complex stochastic dynamics is converted into a simpler one. Then we show the opposite phenomenon whereby the autonomous (without input noise) transition from chaotic order to stochastic disorder is achieved by a static non-invertible non-linearity. We build electronic systems to simulate and produce experimentally all these phenomena.