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An elapsed time model for strongly coupled inhibitory and excitatory neural networks

Abstract : The elapsed time model has been widely studied in the context of mathematical neuroscience with many open questions left. The model consists of an age-structured equation that describes the dynamics of interacting neurons structured by the elapsed time since their last discharge. Our interest lies in highly connected networks leading to strong nonlinearities where perturbation methods do not apply. To deal with this problem, we choose a particular case which can be reduced to delay equations. We prove a general convergence result to a stationary state in the inhibitory and the weakly excitatory cases. Moreover, we prove the existence of particular periodic solutions with jump discontinuities in the strongly excitatory case. Finally, we present some numerical simulations which ilustrate various behaviors, which are consistent with the theoretical results.
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https://hal.archives-ouvertes.fr/hal-03172021
Contributor : Nicolas Torres Connect in order to contact the contributor
Submitted on : Thursday, March 18, 2021 - 1:09:43 PM
Last modification on : Tuesday, September 28, 2021 - 5:16:42 PM
Long-term archiving on: : Monday, June 21, 2021 - 8:49:26 AM

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Maria Caceres, Benoît Perthame, Delphine Salort, Nicolas Torres. An elapsed time model for strongly coupled inhibitory and excitatory neural networks. Physica D: Nonlinear Phenomena, Elsevier, 2021, ⟨10.1016/j.physd.2021.132977⟩. ⟨hal-03172021⟩

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