Book•
Noise-Induced Transitions: Theory and Applications in Physics, Chemistry, and Biology
15 Feb 2007-
TL;DR: The Symbiosis of Noise and Order - Concluding Remarks as discussed by the authors is based on Probability Theory and Markovian Dichotomous Noise: An Exactly Soluble Colored-Noise Case.
Abstract: Elements of Probability Theory.- Stochastic Models of Environmental Fluctuations.- Markovian Diffusion Processes.- Stochastic Differential Equations.- Noise-Induced Nonequilibrium Phase Transitions.- Noise-Induced Transitions in Physics, Chemistry, and Biology.- External Colored Noise.- Markovian Dichotomous Noise: An Exactly Soluble Colored-Noise Case.- The Symbiosis of Noise and Order - Concluding Remarks.
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TL;DR: Work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.
Abstract: Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.
3,450 citations
Book•
01 Jan 1984TL;DR: In this article, the effect of external random perturbations, "noise", on chemical systems and other open nonlinear systems is studied. But the authors do not consider the effects of external noise on the dynamics of the system.
Abstract: In this paper I will deal with the effect of external random perturbations, “noise”, on chemical systems and other open nonlinear systems. As a concrete example let us consider a CSTR. This is an open system and as such subject to external constraints, namely the concentrations of the chemical species in the feed streams, the flow rate, the stirring rate, the temperature, and the incident light intensity in the case of a photochemical reaction. These external constraints characterize the state of the environment of the open system and will, in general, fluctuate more or less strongly. Such environmental fluctuations are particularly important for natural systems; here random fluctuations are always present and their amplitude is not necessarily small as in laboratory systems. In the latter systems the experimenter will of course try to minimize the effect of random perturbations, though it is impossible to eliminate noise completely. Clearly, random external noise is ubiquitous in open systems, but this fact by itself would hardly warrant a systematic study of the effects of external fluctuations. The question is whether noise is more than a mere nuisance we have to live with. Is there any hope of finding interesting physics? The intuitive, and wrong, answer would be negative: The system averages out rapid fluctuations and the only trace of external noise would be a certain fuzziness in the state of the system. Of course, if the state of the system becomes unstable, the fluctuations initiate the departure from the unstable state. Then the dynamics of the system take over and the system evolves to a new stable state.
1,521 citations
TL;DR: In this article, the behavior of excitable systems driven by Gaussian white noise is reviewed, focusing mainly on those general properties of such systems that are due to noise, and present several applications of their findings in biophysics and lasers.
1,373 citations
TL;DR: Stochastic bistability where the deterministic equations predict monostability and vice-versa is found; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged are found.
988 citations
TL;DR: In this paper, the authors considered a Brownian particle in a periodic potential under heavy damping and showed that if the particle is subject to an external force having time correlations, detailed balance is lost and the particle can exhibit a nonzero net drift speed.
Abstract: We consider a Brownian particle in a periodic potential under heavy damping. The second law forbids it from displaying any net drift speed, even if the symmetry of the potential is broken. But if the particle is subject to an external force having time correlations, detailed balance is lost and the particle can exhibit a nonzero net drift speed. Thus, broken symmetry and time correlations are sufficient ingredients for transport.
926 citations