Cascade-induced synchrony in stochastically driven neuronal networks

Katherine A. Newhall, Gregor Kovačič, Peter R. Kramer, David Cai

Research output: Contribution to journalArticle

Abstract

Perfect spike-to-spike synchrony is studied in all-to-all coupled networks of identical excitatory, current-based, integrate-and-fire neurons with delta-impulse coupling currents and Poisson spike-train external drive. This synchrony is induced by repeated cascading "total firing events," during which all neurons fire at once. In this regime, the network exhibits nearly periodic dynamics, switching between an effectively uncoupled state and a cascade-coupled total firing state. The probability of cascading total firing events occurring in the network is computed through a combinatorial analysis conditioned upon the random time when the first neuron fires and using the probability distribution of the subthreshold membrane potentials for the remaining neurons in the network. The probability distribution of the former is found from a first-passage-time problem described by a Fokker-Planck equation, which is solved analytically via an eigenfunction expansion. The latter is found using a central limit argument via a calculation of the cumulants of a single neuronal voltage. The influence of additional physiological effects that hinder or eliminate cascade-induced synchrony are also investigated. Conditions for the validity of the approximations made in the analytical derivations are discussed and verified via direct numerical simulations.

Original languageEnglish (US)
Article number041903
JournalPhysical Review E
Volume82
Issue number4
DOIs
StatePublished - Oct 1 2010

Fingerprint

Neuronal Network
Synchrony
neurons
Cascade
Neuron
cascades
Spike
spikes
combinatorial analysis
Probability Distribution
physiological effects
Combinatorial Analysis
Membrane Potential
Eigenfunction Expansion
First Passage Time
Cumulants
Fokker-Planck equation
Fokker-Planck Equation
direct numerical simulation
Impulse

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Newhall, K. A., Kovačič, G., Kramer, P. R., & Cai, D. (2010). Cascade-induced synchrony in stochastically driven neuronal networks. Physical Review E, 82(4), [041903]. https://doi.org/10.1103/PhysRevE.82.041903

Cascade-induced synchrony in stochastically driven neuronal networks. / Newhall, Katherine A.; Kovačič, Gregor; Kramer, Peter R.; Cai, David.

In: Physical Review E, Vol. 82, No. 4, 041903, 01.10.2010.

Research output: Contribution to journalArticle

Newhall, Katherine A. ; Kovačič, Gregor ; Kramer, Peter R. ; Cai, David. / Cascade-induced synchrony in stochastically driven neuronal networks. In: Physical Review E. 2010 ; Vol. 82, No. 4.
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