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Modulating coherence resonance in non-excitable systems by time-delayed feedback

Author

Listed:
  • Paul M. Geffert
  • Anna Zakharova
  • Andrea Vüllings
  • Wolfram Just
  • Eckehard Schöll

Abstract

We propose a paradigmatic model system, a subcritical Hopf normal form subjected to noise and time-delayed feedback, to investigate the impact of time delay on coherence resonance in non-excitable systems. We develop analytical tools to estimate the stationary distribution and the time correlations in nonlinear stochastic delay differential equations. These tools are applied to our model to propose a novel quantity to measure coherence resonance induced by a saddle-node bifurcation of periodic orbits. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Paul M. Geffert & Anna Zakharova & Andrea Vüllings & Wolfram Just & Eckehard Schöll, 2014. "Modulating coherence resonance in non-excitable systems by time-delayed feedback," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(12), pages 1-13, December.
    • Handle: RePEc:spr:eurphb:v:87:y:2014:i:12:p:1-13:10.1140/epjb/e2014-50541-2
    DOI: 10.1140/epjb/e2014-50541-2
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    Citations

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    Cited by:

    1. Korneev, Ivan & Zakharova, Anna & Semenov, Vladimir V., 2024. "Lévy noise-induced coherence resonance: Numerical study versus experiment," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Xu, Pengfei & Jin, Yanfei, 2020. "Coherence and stochastic resonance in a second-order asymmetric tri-stable system with memory effects," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Semenov, Vladimir V. & Bukh, Andrei V. & Semenova, Nadezhda, 2023. "Delay-induced self-oscillation excitation in the Fitzhugh–Nagumo model: Regular and chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Semenov, Vladimir V., 2018. "Self-oscillation excitation under condition of positive dissipation in a state-dependent potential well," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 358-364.
    5. Guo, Qin & Sun, Zhongkui & Xu, Wei, 2019. "Delay-induced transitions in the birhythmic biological model under joint noise sources," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 337-348.
    6. Masoliver, Maria & Masoller, Cristina & Zakharova, Anna, 2021. "Control of coherence resonance in multiplex neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).

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    Keywords

    Statistical and Nonlinear Physics;

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