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Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size.

Pierre Guiraud 1 Etienne Tanré 2
2 TOSCA - TO Simulate and CAlibrate stochastic models
CRISAM - Inria Sophia Antipolis - Méditerranée , IECL - Institut Élie Cartan de Lorraine : UMR7502
Abstract : In the present paper, we study the synchronization in a model of neural network which can be considered as a noisy version of the model of \citet{mirollo1990synchronization}, namely, fully-connected and totally excitatory integrate and fire neural network with Gaussian white noises. Using a large deviation principle, we prove the stability of the synchronized state under stochastic perturbations. Then, we give a lower bound on the probability of synchronization for networks which are not initially synchronized. This bound shows the robustness of the emergence of synchronization in presence of small stochastic perturbations.
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Pierre Guiraud, Etienne Tanré. Stability of synchronization under stochastic perturbations in leaky integrate and fire neural networks of finite size.. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2019, 24 (9), pp.5183--5201. ⟨10.3934/dcdsb.2019056⟩. ⟨hal-01370609⟩

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