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Pré-Publication, Document De Travail Année : 2016

Adaptive oscillatory neurons generate periodic bursting: analytic and numerical study of the attractor dynamics

Résumé

Several experimental and numerical studies have observed that populations of oscillatory neurons can synchronize and converge to an dynamical attractor composed of periodic bursts which involve the whole network. We show here that a sufficient condition for this phenomenon to occur is the presence of an excitatory population of oscillatory neurons displaying spike-driven adaptation, which was observed for cultured pyramidal neurons from the cortex or the hippocampus. More than just synchronization – which takes place even for weak coupling – bursting occurs for stronger coupling as the adaptive neurons switch from their initial adaptive spiking to an intermittent burst-like behavior. Addition of inhibitory neurons or plastic synapses can then modulate this dynamics in many ways but is not necessary for its appearance. After discussing the origin of the bursting behavior, we provide a detailed analytic and numerical description of such dynamics, as well as the evolution of its properties depending on the neuronal and synaptic parameters. This allows us to explain the change in the neuronal dynamics and the phenomenon underlying the termination of a burst. We based our study on a mean-field model for adaptive exponential integrate-and-fire (aEIF or AdEx) neurons, thanks to which we discuss the related biological phenomena and the relevance of the explored region of parameter space. A sufficient condition for synchronous bursting in neuronal population is the existence of a population of excitatory neurons displaying spike-driven adaptation and oscillatory behavior. For strong enough coupling, the adaptive neurons not only synchronize but switch from their initial regular spiking to an emergent and intermittent burst-like behavior. Using a 2D dynamical system, we provide a detailed analytic and numerical description of such dynamics based on a simplified mean-field model. This leads to a minimal model, based on a hypothesis that can be tested experimentally, which not only reproduces the biological observations but also provides an explanation to the underlying phenomena involved in synchronous bursting. Indeed we propose possible mechanisms for both the initiation and termination of a collective burst as well as analytic results to predict the properties of the global activity and its evolution depending on neuronal and synaptic parameters.
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Dates et versions

hal-01401843 , version 1 (23-11-2016)
hal-01401843 , version 2 (13-02-2024)

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  • HAL Id : hal-01401843 , version 1

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Tanguy Fardet, Mathieu Ballandras, Samuel Bottani, Stéphane Métens, Pascal Monceau. Adaptive oscillatory neurons generate periodic bursting: analytic and numerical study of the attractor dynamics. 2016. ⟨hal-01401843v1⟩
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