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Noise-driven transition to quasi-deterministic limit cycle dynamics in excitable systems

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Cyrill B. Muratov, Eric Vanden-Eijnden, Weinan E

Quantitative Methods · Submitted 10 Dec 2003

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle behavior, absent without noise.

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arXiv IDq-bio/0312013 (version 1)
Pith IDLWDT5MZI, Pith's permanent record of this paper and its review
CitationCyrill B. Muratov, Eric Vanden-Eijnden, Weinan E. "Noise-driven transition to quasi-deterministic limit cycle dynamics in excitable systems." arXiv:q-bio/0312013 (2003). https://pith.science/paper/LWDT5MZI
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,617 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.03 · controlled comparison 0.43 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.29 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle behavior, absent without noise. The limit cycle is established at a critical value of the amplitude of the noise, and its period is nontrivially determined by the relationship between the noise amplitude and the time scale ratio. It is argued that this effect might provide a mechanism by which the function of biological systems operating in noisy environments can be robustly controlled by the level of the noise.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. contribution 0.72 0.79 0.03 asserted 0.57
s1 It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle behavior, absent without noise. result 1.00 0.92 0.81 asserted 1.00
s2 The limit cycle is established at a critical value of the amplitude of the noise, and its period is nontrivially determined by the relationship between the noise amplitude and the time scale ratio. result 1.00 0.89 0.28 asserted 1.00
s3 It is argued that this effect might provide a mechanism by which the function of biological systems operating in noisy environments can be robustly controlled by the level of the noise. interpretation 1.00 0.29 0.26 speculative 0.79

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.74.

What was examined, and what was not

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  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

The effect of small-amplitude noise on excitable systems with large time-scale separation is analyzed. It is found that small random perturbations of the fast excitatory variable result in the onset of a quasi-deterministic limit cycle behavior, absent without noise. The limit cycle is established at a critical value of the amplitude of the noise, and its period is nontrivially determined by the relationship between the noise amplitude and the time scale ratio. It is argued that this effect might provide a mechanism by which the function of biological systems operating in noisy environments can be robustly controlled by the level of the noise.

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