Sequence of pseudoequilibria describes the long-time behavior of the nonlinear noisy leaky integrate-and-fire model with large delay
Year: 2024
Type: article
Abstract: There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the membrane potential. We introduce a sequence of states, which we call pseudoequilibria, and give evidence of their defining role in the behavior of the NNLIF system when a significant synaptic delay is considered. The advantage is that these states are determined solely by the system's parameters and are derived from a sequence of firing rates that result from solving a recurrence equation. We propose a strategy to show convergence to an equilibrium for a weakly connected system with large transmission delay, based on following the sequence of pseudoequilibria. Unlike direct entropy dissipation methods, this technique allows us to see how a large delay favors convergence. We present a detailed numerical study to support our results. This study helps us understand, among other phenomena, the appearance of periodic solutions in strongly inhibitory networks.
Source: Physical review. E
Institution: Universidad de Granada
Language: English
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: green
Awards: G1175115578, G121809054, G1462035462, G1622782223, G1855990336, G2193086574, G2262748287, G2290243270, G2309174360, G2660406951, G279363373, G2894098041, G300979063, G34346518, G3480869486, G3681338154, G3991634671, G410571670, G425668148, G430777504, G451917667, G5074850796, G5080475149, G5421974903, G5539308778, G567365627, G5805502524, G5967599077, G7084143925, G8434830731, G8544902995, G897484643, G929308097, G99296377
OpenAlex ID: W4405108788