Mode Hopping in Oscillating Systems with Stochastic Delays

Klinshov, Vladimir; Shchapin, Dmitry; D'Huys, Otti

doi:10.1103/physrevlett.125.034101

Cited by 4 publications

(7 citation statements)

References 52 publications

(29 reference statements)

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“…In order to keep ψ 20 constant as the coupling increases, we adjust the delay to τ = 20.75 − 20 2π . The lifetimes only depend weakly on the delay, and this dependency disappears as the delay increases; we have shown this numerically in earlier work, 29 and this property appears in the linear theory [Eq. (29)] as well as for continuous coupling.…”

Section: Simulationssupporting

confidence: 69%

“…23,24 Delays were shown to cause multistability in recurrent neural loops 25,26 and lead to the emergence of complex high-period and chaotic behavior in oscillatory systems with pulse feedback. 27,28 In this paper, we extend our earlier work 29 and show that pulseinteracting systems are well suited to study the effect of stochastic fluctuations of different types, thanks to the discrete nature of the coupling. In particular, we consider an oscillator with pulse delayed coupling and introduce noise of two types: (i) phase noise acting on the oscillator and (ii) stochastic fluctuations of the coupling delay.…”

Section: Introductionsupporting

confidence: 59%

“…( 42) does not provide a good quantitative approximation for the width of the frequency distribution. However, the different dependency on both types of noise does explain some qualitative features we found in earlier work 29 for nonlinear PRCs.…”

Section: Chaosmentioning

confidence: 52%

“…A similar effect was described numerically already in Ref. 29; however, in the case of phase noise, the theoretical explanation relied on a comparison with the continuously coupled system, which is only valid for weak coupling. In particular, this did not allow us to discover the decrease of the lifetimes for strong coupling in the case of phase noise.…”

Section: Introductionmentioning

confidence: 54%

“…In contrast to Ref. 29, this model contains both types of noise simultaneously. We show that the map-based approach still can be applied to describe the noisy dynamics of the system and propose the event-based integration scheme that we use for numerical simulations of the system.…”

Section: Introductionmentioning

confidence: 94%

See 4 more Smart Citations

Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach

Klinshov

D'Huys

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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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Section: Simulationssupporting

confidence: 69%

Section: Introductionsupporting

confidence: 59%

Section: Chaosmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 94%

See 3 more Smart Citations

Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach

Klinshov

D'Huys

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

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View full text Add to dashboard Cite

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Constructive role of shot noise in the collective dynamics of neural networks

Klinshov

Smelov

Kirillov

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Finite-size effects may significantly influence the collective dynamics of large populations of neurons. Recently, we have shown that in globally coupled networks these effects can be interpreted as additional common noise term, the so-called shot noise, to the macroscopic dynamics unfolding in the thermodynamic limit. Here, we continue to explore the role of the shot noise in the collective dynamics of globally coupled neural networks. Namely, we study the noise-induced switching between different macroscopic regimes. We show that shot noise can turn attractors of the infinitely large network into metastable states whose lifetimes smoothly depend on the system parameters. A surprising effect is that the shot noise modifies the region where a certain macroscopic regime exists compared to the thermodynamic limit. This may be interpreted as a constructive role of the shot noise since a certain macroscopic state appears in a parameter region where it does not exist in an infinite network.

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Adaptive myelination causes slow oscillations in recurrent neural loops

Klinshov,

Nekorkin

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The brain is known to be plastic, i.e., capable of changing and reorganizing as it develops and accumulates experience. Recently, a novel form of brain plasticity was described which is activity-dependent myelination of nerve fibers. Since the speed of propagation of action potentials along axons depends significantly on their degree of myelination, this process leads to adaptive change of axonal delays depending on the neural activity. To understand the possible influence of the adaptive delays on the behavior of neural networks, we consider a simple setup, a neuronal oscillator with delayed feedback. We show that introducing the delay plasticity into this circuit can lead to the occurrence of slow oscillations which are impossible with a constant delay.

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Mode Hopping in Oscillating Systems with Stochastic Delays

Cited by 4 publications

References 52 publications

Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach

Noise-induced switching in an oscillator with pulse delayed feedback: A discrete stochastic modeling approach

Constructive role of shot noise in the collective dynamics of neural networks

Adaptive myelination causes slow oscillations in recurrent neural loops

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