English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We investigate the dynamics of large-scale interacting neural populations,composed of conductance based, spiking model neurons with modifiable synapticconnection strengths, which are possibly also subjected to external noisycurrents. The network dynamics is controlled by a set of neural populationprobability distributions ($\mathrm{PPD}$)which are constructed along the samelines as in the Klimontovich approach to the kinetic theory of plasmas. Anexact non-closed, nonlinear, system of integro-partial differential equationsis derived for the $\mathrm{PPD}$s. As is customary, a closing procedure leadsto a mean field limit. The equations we have obtained are of the same type asthose which have been recently derived using rigorous techniques of probabilitytheory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planckequations, which are only valid in the limit of infinite size networks,actually shows that the statistical measures as obtained from $\mathrm{PPD}$sare in good agreement with those obtained through direct integration of thestochastic dynamical system for large but finite size networks. Althoughnumerical solutions have been obtained in the case of Fitzhugh-Nagumo modelneurons, the theory can be readily applied to systems of Hodgkin-Huxley typemodel neurons of arbitrary dimension.

Mean field analysis of large-scale interacting populations of stochastic conductance-based spiking neurons using the Klimontovich method