Stochastic resonance without external periodic force

Hu, Gang; Ditzinger, Thomas; Ning, Chao; Haken, Hermann

doi:10.1103/physrevlett.71.807

Cited by 667 publications

(301 citation statements)

References 23 publications

Supporting

Mentioning

289

Contrasting

Order By: Relevance

“…However, most of the papers concentrate on so called stochastic resonance -the response of s bistable system to a periodic external force in the presence of noise [1,8,7]. Yet in many nonlinear systems coherent transitions are not stimulated by an external force [12] and this is also probably the case of social systems.…”

Section: Discussionmentioning

confidence: 99%

Opinion dynamics as a movement in a bistable potential

Nyczka

Cisło

Sznajd-Weron

2012

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

In this paper we investigate the model of opinion dynamics with anticonformity on a complete graph. We show that below some threshold value of anticonformal behavior spontaneous reorientations occur between two stable states. Dealing with a complete graph allows us also for analytical treatment. We show that opinion dynamics can be understood as a movement of a public opinion in a symmetric bistable effective potential. We focus also on the spontaneous transitions between stable states and show that a typical waiting time can be observed.

show abstract

Section: Discussionmentioning

confidence: 99%

Opinion dynamics as a movement in a bistable potential

Nyczka

Cisło

Sznajd-Weron

2012

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

show abstract

“…An exaggerated input of noise washes out the periodic oscillation and leads to a random output. This delicate balance between noise and nonlinear dynamics is known as autonomous stochastic resonance (Gang et al 1993;Longtin 1997) or coherence resonance (Pikovsky and Kurths 1997;Lindner and Schimansky-Geier 1999;Pradines et al 1999). Coherence resonance can be explained in terms of a noisy precursor to deterministic bifurcations such as Hopf bifurcations (Neiman et al 1997) or homoclinic and heteroclinic bifurcations (Stone and Holmes 1989;Stone and Armbruster 1999).…”

Section: Noise-induced Oscillations: Coherence Resonancementioning

confidence: 99%

Coherent Resonant Millennial-Scale Climate Oscillations Triggered by Massive Meltwater Pulses

Timmermann¹,

Gildor²,

Schulz³

et al. 2003

J. Climate

130

140

View full text Add to dashboard Cite

The role of mean and stochastic freshwater forcing on the generation of millennial-scale climate variability in the North Atlantic is studied using a low-order coupled atmosphere-ocean-sea ice model. It is shown that millennial-scale oscillations can be excited stochastically, when the North Atlantic Ocean is fresh enough. This finding is used in order to interpret the aftermath of massive iceberg surges (Heinrich events) in the glacial North Atlantic, which are characterized by an excitation of Dansgaard-Oeschger events. Based on model results, it is hypothesized that Heinrich events trigger Dansgaard-Oeschger cycles and that furthermore the occurrence of Heinrich events is dependent on the accumulated climatic effect of a series of Dansgaard-Oeschger events. This scenario leads to a coupled ocean-ice sheet oscillation that shares many similarities with the Bond cycle. Further sensitivity experiments reveal that the timescale of the oscillations can be decomposed into stochastic, linear, and nonlinear deterministic components. A schematic bifurcation diagram is used to compare theoretical results with paleoclimatic data.

show abstract

“…A moderate level of noise, on the other hand, is able to evoke pulses frequently, as soon as the refractory time following the previous pulse (characteristic of all excitable systems) has elapsed, and thus leads to a substantially periodic behavior, with a period basically given by the refractory time. Such somewhat counterintuitive effect of noise has been termed coherence resonance or, more appropriately, stochastic coherence [14][15][16]. The goal of this paper is to show that stochastic coherence can be invoked, together with the noise-induced stabilization effect discussed above, to provide a minimal mechanism for the generation of polymodal distributions of cycle lengths in an otherwise periodic behavior.…”

Section: Introductionmentioning

confidence: 99%

Optimizing periodicity and polymodality in noise-induced genetic oscillators

2011

View full text Add to dashboard Cite

Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities in the form of period skippings, which lead to polymodal distributions of cycle lengths. A recently proposed mechanism that accounts for this quantized behavior is the stabilization of a Hopf-unstable state by molecular noise. Here we investigate the effect of varying noise in a model system, namely an excitable activator-repressor genetic circuit, that displays this noise-induced stabilization effect. Our results show that an optimal noise level enhances the regularity (coherence) of the cycles, in a form of coherence resonance. Similar noise levels also optimize the multimodal nature of the cycle lengths. Together, these results illustrate how molecular noise within a minimal gene regulatory motif confers robust generation of polymodal patterns of periodicity.

show abstract

Stochastic resonance without external periodic force

Cited by 667 publications

References 23 publications

Opinion dynamics as a movement in a bistable potential

Opinion dynamics as a movement in a bistable potential

Coherent Resonant Millennial-Scale Climate Oscillations Triggered by Massive Meltwater Pulses

Optimizing periodicity and polymodality in noise-induced genetic oscillators

Contact Info

Product

Resources

About