### 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 language | English (US) |
---|---|

Article number | 041903 |

Journal | Physical Review E |

Volume | 82 |

Issue number | 4 |

DOIs | |

State | Published - Oct 1 2010 |

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### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 82, no. 4, 041903. https://doi.org/10.1103/PhysRevE.82.041903

}

TY - JOUR

T1 - Cascade-induced synchrony in stochastically driven neuronal networks

AU - Newhall, Katherine A.

AU - Kovačič, Gregor

AU - Kramer, Peter R.

AU - Cai, David

PY - 2010/10/1

Y1 - 2010/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78651264671&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78651264671&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.82.041903

DO - 10.1103/PhysRevE.82.041903

M3 - Article

C2 - 21230309

AN - SCOPUS:78651264671

VL - 82

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4

M1 - 041903

ER -