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

Klinshov, Vladimir; Smelov, Pavel S.; Kirillov, Sergey

doi:10.1063/5.0147409

Cited by 7 publications

References 67 publications

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

Eydam,

Franović,

Kang

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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

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

Eydam,

Franović,

Kang

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Collective dynamics and shot-noise-induced switching in a two-population neural network

Kirillov,

Smelov,

Klinshov

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Neural mass models are a powerful tool for modeling of neural populations. Such models are often used as building blocks for the simulation of large-scale neural networks and the whole brain. Here, we carry out systematic bifurcation analysis of a neural mass model for the basic motif of various neural circuits, a system of two populations, an excitatory, and an inhibitory ones. We describe the scenarios for the emergence of complex collective behavior, including chaotic oscillations and multistability. We also compare the dynamics of the neural mass model and the exact microscopic system and show that their agreement may be far from perfect. The discrepancy can be interpreted as the action of the so-called shot noise originating from finite-size effects. This shot noise can lead to the blurring of the neural mass dynamics or even turn its attractors into metastable states between which the system switches recurrently.

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Regime switching in coupled nonlinear systems: Sources, prediction, and control—Minireview and perspective on the Focus Issue

Franović,

Eydam,

Eroglu

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Regime switching, the process where complex systems undergo transitions between qualitatively different dynamical states due to changes in their conditions, is a widespread phenomenon, from climate and ocean circulation, to ecosystems, power grids, and the brain. Capturing the mechanisms that give rise to isolated or sequential switching dynamics, as well as developing generic and robust methods for forecasting, detecting, and controlling them is essential for maintaining optimal performance and preventing dysfunctions or even collapses in complex systems. This Focus Issue provides new insights into regime switching, covering the recent advances in theoretical analysis harnessing the reduction approaches, as well as data-driven detection methods and non-feedback control strategies. Some of the key challenges addressed include the development of reduction techniques for coupled stochastic and adaptive systems, the influence of multiple timescale dynamics on chaotic structures and cyclic patterns in forced systems, and the role of chaotic saddles and heteroclinic cycles in pattern switching in coupled oscillators. The contributions further highlight deep learning applications for predicting power grid failures, the use of blinking networks to enhance synchronization, creating adaptive strategies to control epidemic spreading, and non-feedback control strategies to suppress epileptic seizures. These developments are intended to catalyze further dialog between the different branches of complexity.

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

Cited by 7 publications

References 67 publications

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

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

Collective dynamics and shot-noise-induced switching in a two-population neural network

Regime switching in coupled nonlinear systems: Sources, prediction, and control—Minireview and perspective on the Focus Issue

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