Abstract
Stochastic Resonance (SR) is a well known process whereby the transmission of a weak periodic signal through some nonlinear systems can be improved by adding a random perturbation (noise). Unlike the conventional SR, we produce this phenomenon by adding a chaotic perturbation to the system. We study chaotic functions as exact solutions to non‐linear maps and obtain explicit mathematical expressions to generate the chaotic perturbation. The Lyapunov exponent of these functions can be calculated exactly. The signal to noise ratio (SNR) can be amplified for determined intervals of the Lyapunov exponent. This allows one to control the SR by tuning the level of chaos. We present an experimental evidence in a threshold‐type electronic circuit. There exist a common belief that random sequences are produced from very complicated phenomena, making impossible the construction of accurate mathematical models. We show that under appropriated conditions our chaotic functions can be generalized to produce truly random sequences. We build electronic systems to simulate these functions and produce experimentally the so‐called Deterministic Randomness (DR). The phenomenon is based in the transmission of deterministic signals through some nonlinear systems to generate stochastic dynamics. In particular we show the DR being produced in the coupling of a chaotic system, the Chua’s circuit, with an electronic analogue of the Josephson junction.
Published Version
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