Stochastic Resonance

Stochastic Resonance

1993 | M.I. Dykman, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, S.M. Soskin, N.D. Stein and N.G. Stocks
Stochastic resonance (SR) is a phenomenon in which a weak periodic signal in a nonlinear system can be enhanced by the addition of external noise. This paper reviews SR, emphasizing its description through linear response theory (LRT). LRT is noted for its simplicity, generality, and predictive power, even though it is restricted to the small signal limit. The paper discusses conventional SR in overdamped motion in a bistable potential and two new forms of SR predicted by LRT and observed in electronic experiments. SR arises from the interaction of nonlinearity, fluctuations, and a periodic force. It was first introduced in the context of Earth's ice-age cycles and later demonstrated in electronic circuits and ring lasers. Since then, SR has been observed in various systems, including passive optical systems, electron spin resonance, sensory neurons, and magneto-elastic strips. The paper introduces SR within the framework of LRT, highlighting its general applicability. It describes how LRT can predict new forms of SR in different systems. Section 2 outlines the LRT approach, explaining how the susceptibility of a system determines the signal amplitude and phase lag. Section 3 discusses SR in static double-well potentials, showing that the signal-to-noise ratio increases with noise intensity, indicating SR. Section 4 presents a new form of SR involving periodic attractors, where stochastic amplification occurs at high frequencies. Section 5 describes SR in monostable systems, showing that even systems without bistability can exhibit SR if their susceptibility increases with noise intensity. Section 6 concludes that LRT provides a good description of both conventional and new forms of SR, even for larger signal amplitudes. The paper emphasizes the importance of LRT in understanding the general behavior of SR in various systems.Stochastic resonance (SR) is a phenomenon in which a weak periodic signal in a nonlinear system can be enhanced by the addition of external noise. This paper reviews SR, emphasizing its description through linear response theory (LRT). LRT is noted for its simplicity, generality, and predictive power, even though it is restricted to the small signal limit. The paper discusses conventional SR in overdamped motion in a bistable potential and two new forms of SR predicted by LRT and observed in electronic experiments. SR arises from the interaction of nonlinearity, fluctuations, and a periodic force. It was first introduced in the context of Earth's ice-age cycles and later demonstrated in electronic circuits and ring lasers. Since then, SR has been observed in various systems, including passive optical systems, electron spin resonance, sensory neurons, and magneto-elastic strips. The paper introduces SR within the framework of LRT, highlighting its general applicability. It describes how LRT can predict new forms of SR in different systems. Section 2 outlines the LRT approach, explaining how the susceptibility of a system determines the signal amplitude and phase lag. Section 3 discusses SR in static double-well potentials, showing that the signal-to-noise ratio increases with noise intensity, indicating SR. Section 4 presents a new form of SR involving periodic attractors, where stochastic amplification occurs at high frequencies. Section 5 describes SR in monostable systems, showing that even systems without bistability can exhibit SR if their susceptibility increases with noise intensity. Section 6 concludes that LRT provides a good description of both conventional and new forms of SR, even for larger signal amplitudes. The paper emphasizes the importance of LRT in understanding the general behavior of SR in various systems.
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[slides and audio] Stochastic resonance