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Detecting limit cycles in stochastic time series

Author

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  • Martiny, Emil S.
  • Jensen, Mogens H.
  • Heltberg, Mathias S.

Abstract

The emergence of oscillatory behaviour represents fundamental information about the interactions of the underlying system. In biological systems, oscillations have been observed in experimental data, but due to the significant level of noise, it is difficult to characterize whether observed dynamics based on time series, are truly limit cycles. Here, we present a simple three step method to identify the presence of limit cycles in stochastic systems. Considering input from one-dimensional time series, as are typically obtained in experiments, we propose statistical measures to detect the existence of limit cycles. This is tested on models from chemical networks, and we investigate how the underlying dynamics can be separated depending on the noise level and length of the series.

Suggested Citation

  • Martiny, Emil S. & Jensen, Mogens H. & Heltberg, Mathias S., 2022. "Detecting limit cycles in stochastic time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    • Handle: RePEc:eee:phsmap:v:605:y:2022:i:c:s0378437122005854
    DOI: 10.1016/j.physa.2022.127917
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    References listed on IDEAS

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    1. Avigdor Eldar & Michael B. Elowitz, 2010. "Functional roles for noise in genetic circuits," Nature, Nature, vol. 467(7312), pages 167-173, September.
    2. Leung, H.K., 1998. "Stochastic Hopf bifurcation in a biased van der Pol model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 254(1), pages 146-155.
    3. Mathias L. Heltberg & Sandeep Krishna & Mogens H. Jensen, 2019. "On chaotic dynamics in transcription factors and the associated effects in differential gene regulation," Nature Communications, Nature, vol. 10(1), pages 1-10, December.
    4. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
    5. Bashkirtseva, Irina & Ryashko, Lev & Schurz, Henri, 2009. "Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 72-82.
    6. Savaş Tay & Jacob J. Hughey & Timothy K. Lee & Tomasz Lipniacki & Stephen R. Quake & Markus W. Covert, 2010. "Single-cell NF-κB dynamics reveal digital activation and analogue information processing," Nature, Nature, vol. 466(7303), pages 267-271, July.
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