Macroscopic behavior of populations of quadratic integrate-and-fire neurons subject to non-Gaussian white noise

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2024, Номер 34(1)

Опубликована: Янв. 1, 2024

We study macroscopic behavior of populations quadratic integrate-and-fire neurons subject to non-Gaussian noises; we argue that these noises must be α-stable whenever they are delta-correlated (white). For the case additive-in-voltage noise, derive governing equation dynamics characteristic function membrane voltage distribution and construct a linear-in-noise perturbation theory. Specifically for recurrent network with global synaptic coupling, theoretically calculate observables: population-mean firing rate. The theoretical results underpinned by numerical simulation homogeneous heterogeneous populations. possibility generalization pseudocumulant approach fractional α is examined both irrational rational α. This examination seemingly suggests or its modifications employable only integer values α=1 (Cauchy noise) 2 (Gaussian within physically meaningful range (0;2]. Remarkably, analysis indirectly revealed that, Gaussian minimal asymptotically rigorous model reduction involve three pseudocumulants two-pseudocumulant an artificial approximation. explains surprising gain accuracy three-pseudocumulant models as compared ones reported in literature.

Язык: Английский

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Exact low-dimensional description for fast neural oscillations with low firing rates

Physical review. E, Год журнала: 2024, Номер 109(1)

Опубликована: Янв. 31, 2024

Recently, low-dimensional models of neuronal activity have been exactly derived for large networks deterministic, quadratic integrate-and-fire (QIF) neurons. Such firing rate (FRM) describe the emergence fast collective oscillations (>30 Hz) via frequency locking a subset neurons to global oscillation frequency. However, suitability such realistic states is seriously challenged by fact that during episodes oscillations, discharges are often very irregular and low rates compared Here we extend theory derive exact FRM QIF include noise show stochastic displaying at governed same evolution equations as deterministic networks. Our results reconcile two traditionally confronted views on synchronization upgrade applicability broad range biologically states.

Язык: Английский

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Low-dimensional model for adaptive networks of spiking neurons

Physical review. E, Год журнала: 2025, Номер 111(1)

Опубликована: Янв. 24, 2025

We investigate a large ensemble of quadratic integrate-and-fire neurons with heterogeneous input currents and adaptation variables. Our analysis reveals that, for specific class adaptation, termed spike-frequency the high-dimensional system can be exactly reduced to low-dimensional ordinary differential equations, which describes dynamics three mean-field variables: population's firing rate, mean membrane potential, variable. The resulting rate equations (FREs) uncover key generic feature networks adaptation: Both center width distribution neurons' frequencies are reduced, this largely promotes emergence collective synchronization in network. findings further supported by bifurcation FREs, accurately captures spiking neuron network, including phenomena such as oscillations, bursting, macroscopic chaos.

Язык: Английский

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Nonlinear bias of collective oscillation frequency induced by asymmetric Cauchy noise

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2025, Номер 35(2)

Опубликована: Фев. 1, 2025

We report the effect of nonlinear bias frequency collective oscillations sin-coupled phase oscillators subject to individual asymmetric Cauchy noises. The noise asymmetry makes Ott–Antonsen ansatz inapplicable. argue that, for all stable non-Gaussian noises, tail is not only possible (in addition trivial shift distribution median) but also generic in many physical and biophysical setups. For theoretical description effect, we develop a mathematical formalism based on circular cumulants. derivation rigorous asymptotic results can be performed this basis seems infeasible traditional terms moments (the Kuramoto–Daido order parameters). entrainment oscillator frequencies by global reported detail. accuracy low-dimensional cumulant reductions validated with high-accuracy “exact” solutions calculated continued fraction method.

Язык: Английский

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Fluctuation induced intermittent transitions between distinct rhythms in balanced excitatory–inhibitory spiking networks

Chaos Solitons & Fractals, Год журнала: 2025, Номер 196, С. 116321 - 116321

Опубликована: Март 28, 2025

Язык: Английский

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Circular cumulant reductions for macroscopic dynamics of oscillator populations with non-Gaussian noise

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2023, Номер 33(11)

Опубликована: Ноя. 1, 2023

We employ the circular cumulant approach to construct a low dimensional description of macroscopic dynamics populations phase oscillators (elements) subject non-Gaussian white noise. Two-cumulant reduction equations for α-stable noises are derived. The implementation is demonstrated case Kuramoto ensemble with results direct numerical simulation N=1500 and "exact" solution fractional Fokker-Planck equation in Fourier space found be good agreement analytical solutions two feasible model reductions. also illustrate that two-cumulant useful studying bifurcations chimera states hierarchical coupled noisy oscillators.

Язык: Английский

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Desynchronization of large-scale neural networks by stabilizing unknown unstable incoherent equilibrium states

Physics Letters A, Год журнала: 2023, Номер 492, С. 129232 - 129232

Опубликована: Ноя. 17, 2023

Язык: Английский

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Whole brain functional connectivity: Insights from next generation neural mass modelling incorporating electrical synapses

PLoS Computational Biology, Год журнала: 2024, Номер 20(12), С. e1012647 - e1012647

Опубликована: Дек. 5, 2024

The ready availability of brain connectome data has both inspired and facilitated the modelling whole activity using networks phenomenological neural mass models that can incorporate interaction strength tract length between regions. Recently, a new class model been developed from an exact mean field reduction network spiking cortical cell with biophysically realistic chemical synapse. Moreover, this population dynamics naturally electrical synapses. Here we demonstrate ability framework, when combined Human Connectome Project, to generate patterns functional connectivity (FC) type observed in magnetoencephalography magnetic resonance neuroimaging. Some limited explanatory power is obtained via eigenmode description frequency-specific FC patterns, linear stability analysis steady state neigbourhood Hopf bifurcation. However, direct numerical simulations show empirical more faithfully recapitulated nonlinear regime, exposes key role gap junction coupling generating empirically-observed activity, associated their evolution. Thereby, emphasise importance maintaining known links biological reality developing multi-scale dynamics. As tool for study dynamic presented here further provide suite C++ codes efficient, user friendly, simulation multiple delayed interactions.

Язык: Английский

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Exact low-dimensional description for fast neural oscillations with low-firing rates

arXiv (Cornell University), Год журнала: 2022, Номер unknown

Опубликована: Янв. 1, 2022

Recently, low-dimensional models of neuronal activity have been exactly derived for large networks deterministic, Quadratic Integrate-and-Fire (QIF) neurons. Such firing rate (FRM) describe the emergence fast collective oscillations (>30~Hz) via frequency-locking a subset neurons to global oscillation frequency. However, suitability such realistic states is seriously challenged by fact that during episodes oscillations, discharges are often very irregular and low rates compared Here we extend theory derive exact FRM QIF include noise, show stochastic displaying at governed same evolution equations as deterministic networks. Our results reconcile two traditionally confronted views on synchronization, upgrade applicability broad range biologically states.

Язык: Английский

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Control of seizure-like dynamics in neuronal populations with excitability adaptation related to ketogenic diet

Chaos An Interdisciplinary Journal of Nonlinear Science, Год журнала: 2024, Номер 34(5)

Опубликована: Май 1, 2024

We consider a heterogeneous, globally coupled population of excitatory quadratic integrate-and-fire neurons with excitability adaptation due to metabolic feedback associated ketogenic diet, form therapy for epilepsy. Bifurcation analysis three-dimensional mean-field system derived in the framework next-generation neural mass models allows us explain scenarios and suggest control strategies transitions between neurophysiologically desired asynchronous states synchronous, seizure-like featuring collective oscillations. reveal two qualitatively different onset synchrony. For weaker couplings, bistability region lower- higher-activity unfolds from cusp point, oscillations emerge via supercritical Hopf bifurcation. stronger one finds seven co-dimension bifurcation points, including pairs Bogdanov–Takens generalized such that both undergo oscillations, hysteresis jump-like behavior observed vicinity subcritical bifurcations. demonstrate three mechanisms switching synchronous states, involving parametric perturbation adenosine triphosphate (ATP) production rate, external stimulation currents, or pulse-like ATP shocks, indicate potential therapeutic advantage hysteretic scenarios.

Язык: Английский

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