Scaling concepts in periodically modulated noisy systems

We show that scaling arguments are very useful to analyze the dynamics of periodically modulated noisy systems. Information about the behavior of the relevant quantities, such as the signal-to-noise ratio, upon variations of the noise level, can be obtained by analyzing the symmetries and invariances of the system. In this way, it is possible to predict diverse physical manifestations of the cooperative behavior between noise and input signal, as for instance stochastic resonance, spatiotemporal stochastic resonance, and stochastic multiresonance.

[1]  Spatiotemporal stochastic resonance in the Swift-Hohenberg equation , 1997, cond-mat/9702205.

[2]  John B. Shoven,et al.  I , Edinburgh Medical and Surgical Journal.

[3]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[4]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[5]  Hexagonal and roll flow patterns in temporally modulated Rayleigh-Bénard convection. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[6]  G. Vojta,et al.  Fractal Concepts in Surface Growth , 1996 .

[7]  A. Fisher,et al.  The Theory of critical phenomena , 1992 .

[8]  J. M. G. Vilar,et al.  Effect of the output of the system in signal detection , 1997, cond-mat/9703015.

[9]  M. Feigenbaum.  Quantitative universality for a class of nonlinear transformations , 1978 .

[10]  Kurt Wiesenfeld,et al.  Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs , 1995, Nature.

[11]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[12]  Vilar,et al.  Divergent Signal-to-Noise Ratio and Stochastic Resonance in Monostable Systems. , 1996, Physical review letters.

[13]  R. Mantegna,et al.  Scaling behaviour in the dynamics of an economic index , 1995, Nature.

[14]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[15]  Bulsara,et al.  Array enhanced stochastic resonance and spatiotemporal synchronization. , 1995, Physical review letters.

[16]  J. Swift,et al.  Hydrodynamic fluctuations at the convective instability , 1977 .

[17]  P. Hohenberg,et al.  Effects of additive noise at the onset of Rayleigh-Bénard convection. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[18]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[19]  Stochastic influences on pattern formation in Rayleigh-Bénard convection: Ramping experiments. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[20]  Stochastic resonance in a dipole. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Rosario N. Mantegna,et al.  Turbulence and financial markets , 1996, Nature.

[22]  P. Kloeden,et al.  Numerical Solution of Stochastic Differential Equations , 1992 .

[23]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[24]  Santucci,et al.  Stochastic resonance in bistable systems. , 1989, Physical review letters.

[25]  J. M. G. Vilar,et al.  Stochastic Multiresonance , 1997 .

[26]  D. Talay.  Numerical solution of stochastic differential equations , 1994 .

[27]  R. Haberlandt.  Introduction to nonlinear science , 1996 .

[28]  Leo P. Kadanoff,et al.  Scaling and universality in statistical physics , 1990 .

[29]  S. Fauve,et al.  Stochastic resonance in a bistable system , 1983 .

[30]  A. Barabasi,et al.  Fractal Concepts in Surface Growth: Frontmatter , 1995 .

[31]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[32]  Hänggi,et al.  Coherent and incoherent quantum stochastic resonance. , 1996, Physical review letters.

[33]  Sergey M. Bezrukov,et al.  Stochastic resonance in non-dynamical systems without response thresholds , 1997, Nature.

[34]  Bulsara,et al.  Time-interval sequences in bistable systems and the noise-induced transmission of information by sensory neurons. , 1991, Physical review letters.

[35]  Bulsara,et al.  Spatiotemporal stochastic resonance in a phi4 model of kink-antikink nucleation. , 1996, Physical review letters.

[36]  Frank Moss,et al.  Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance , 1993, Nature.

[37]  A. Barabasi,et al.  Fractal concepts in surface growth , 1995 .

[38]  Michael V Berry.  Review of Would-be worlds: how simulation is changing the frontiers of science by Casti, J , 1997 .

[39]  Werner Römisch,et al.  Numerical Solution of Stochastic Differential Equations (Peter E. Kloeden and Eckhard Platen) , 1995, SIAM Rev..

[40]  Wiesenfeld,et al.  Stochastic resonance on a circle. , 1994, Physical review letters.

[41]  Ditto,et al.  Stochastic Resonance in a Neuronal Network from Mammalian Brain. , 1996, Physical review letters.

[42]  Hans Jürgen Herrmann.  Fracture patterns and scaling laws , 1990 .

[43]  F. Moss,et al.  Non-Dynamical Stochastic Resonance: Theory and Experiments with White and Arbitrarily Coloured Noise , 1995 .

[44]  Roy,et al.  Observation of stochastic resonance in a ring laser. , 1988, Physical review letters.