We study the dynamics of an oscillatory system with pulse delayed feedback and noise of two types: (i) phase noise acting on the oscillator and (ii) stochastic fluctuations of the feedback delay. Using an event-based approach, we reduce the system dynamics to a stochastic discrete map. For weak noise, we find that the oscillator fluctuates around a deterministic state, and we derive an autoregressive model describing the system dynamics. For stronger noise, the oscillator demonstrates noise-induced switching between various deterministic states; our theory provides a good estimate of the switching statistics in the linear limit. We show that the robustness of the system toward this switching is strikingly different depending on the type of noise. We compare the analytical results for linear coupling to numerical simulations of nonlinear coupling and find that the linear model also provides a qualitative explanation for the differences in robustness to both types of noise. Moreover, phase noise drives the system toward higher frequencies, while stochastic delays do not, and we relate this effect to our theoretical results.
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September 2022
Research Article|
September 26 2022
Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach
Special Collection:
Non-smooth Dynamics
Vladimir V. Klinshov
;
Vladimir V. Klinshov
a)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
1
Institute of Applied Physics of the Russian Academy of Sciences
, 46 Ul’yanov Street, Nizhny Novgorod 603950, Russia
2
Higher School of Economics, National Research University
, 25/12 Bol’shaya Pecherskaya Street, Nizhny Novgorod 603155, Russia
a)Author to whom correspondence should be addressed: vladimir.klinshov@ipfran.ru
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Otti D’Huys
Otti D’Huys
b)
(Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing)
3
Department of Applied Computing Sciences, Maastricht University
, P.O. Box 616, 6200 MD Maastricht, The Netherlands
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a)Author to whom correspondence should be addressed: vladimir.klinshov@ipfran.ru
b)
Electronic mail: o.dhuys@maastrichtuniversity.nl
Note: This article is part of the Focus Issue, Non-smooth Dynamics.
Chaos 32, 093141 (2022)
Article history
Received:
May 26 2022
Accepted:
August 22 2022
Citation
Vladimir V. Klinshov, Otti D’Huys; Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach. Chaos 1 September 2022; 32 (9): 093141. https://doi.org/10.1063/5.0100698
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