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García‐Ojalvo, Jordi; Schimansky‐Geier, Lutz

doi:10.1023/a:1026493517549

Cited by 15 publications

(2 citation statements)

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“…While noise happens on the small length scales and short time scales of a system, it may trigger events on a global scale. One of the most important functions of noise for macroscopic dynamics arises from its combination with thresholds [38][39][40]. These are defined by the observation that the dynamics of a system remains close to a stable state as long as it does not cross the threshold value, and an actively amplified deviation from this state happens when the threshold is crossed.…”

Section: Introductionmentioning

confidence: 99%

The stretch to stray on time: Resonant length of random walks in a transient

Falcke

Friedhoff

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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First-passage times in random walks have a vast number of diverse applications in physics, chemistry, biology, and finance. In general, environmental conditions for a stochastic process are not constant on the time scale of the average first-passage time or control might be applied to reduce noise. We investigate moments of the first-passage time distribution under an exponential transient describing relaxation of environmental conditions. We solve the Laplace-transformed (generalized) master equation analytically using a novel method that is applicable to general state schemes. The first-passage time from one end to the other of a linear chain of states is our application for the solutions. The dependence of its average on the relaxation rate obeys a power law for slow transients. The exponent ν depends on the chain length N like ν=-N/(N+1) to leading order. Slow transients substantially reduce the noise of first-passage times expressed as the coefficient of variation (CV), even if the average first-passage time is much longer than the transient. The CV has a pronounced minimum for some lengths, which we call resonant lengths. These results also suggest a simple and efficient noise control strategy and are closely related to the timing of repetitive excitations, coherence resonance, and information transmission by noisy excitable systems. A resonant number of steps from the inhibited state to the excitation threshold and slow recovery from negative feedback provide optimal timing noise reduction and information transmission.

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Section: Introductionmentioning

confidence: 99%

The stretch to stray on time: Resonant length of random walks in a transient

Falcke

Friedhoff

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Noise is able to prevent this decay, as can be seen by writing an effective model with a zero-mean noise, as has been made in the previous section. It is easy to see that an optimal value of noise intensity renders the effective potential of this model symmetric [34], which allows sustained propagation of pulses through the system.…”

Section: Noise-induced Propagationmentioning

confidence: 99%

Noise-Induced Order in Extended Systems: A Tutorial

Sancho

García‐Ojalvo

Lecture Notes in Physics

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External fluctuations have a wide variety of constructive effects on the dynamical behavior of spatially extended systems, as described by stochastic partial differential equations. A set of paradigmatic situations exhibiting such effects are briefly reviewed in this paper, in an attempt to provide a concise but thorough introduction to this active field of research, and at the same time an overview of its current status. This work is dedicated to Lutz Schimansky-Geier on the occassion of his 50th anniversary. Through the years, Prof. Schimansky-Geier has made important contributions to the field of spatiotemporal stochastic dynamics, including seminal investigations in the early 1990's on noise effects in front propagation, and studies of noise-induced phase transitions and noise-sustained structures in excitable media, among others. ⋆ From "

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