Time evolution of a mean-field generalized contact process

Logan Chariker; Joel L. Lebowitz

doi:10.1088/1742-5468/ac4985

Time evolution of a mean-field generalized contact process

Logan Chariker, Joel L. Lebowitz

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We investigate the macroscopic time evolution and stationary states of a mean field discrete voltage neuron model, or equivalently, a generalized contact process in Rd. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a model of neurons with discrete voltages evolving by a stochastic integrate and fire mechanism. We obtain a complete solution in the spatially uniform case and partial solutions in the general case. The system has one or more fixed points and also traveling wave solutions.

Original language	English (US)
Article number	023502
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2022
Issue number	2
DOIs	https://doi.org/10.1088/1742-5468/ac4985
State	Published - Feb 1 2022

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

computational neuroscience
neuronal networks
population dynamics
stochastic processes

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10.1088/1742-5468/ac4985

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N2 - We investigate the macroscopic time evolution and stationary states of a mean field discrete voltage neuron model, or equivalently, a generalized contact process in Rd. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a model of neurons with discrete voltages evolving by a stochastic integrate and fire mechanism. We obtain a complete solution in the spatially uniform case and partial solutions in the general case. The system has one or more fixed points and also traveling wave solutions.

AB - We investigate the macroscopic time evolution and stationary states of a mean field discrete voltage neuron model, or equivalently, a generalized contact process in Rd. The model is described by a coupled set of nonlinear integral-differential equations. It was inspired by a model of neurons with discrete voltages evolving by a stochastic integrate and fire mechanism. We obtain a complete solution in the spatially uniform case and partial solutions in the general case. The system has one or more fixed points and also traveling wave solutions.

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KW - population dynamics

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Time evolution of a mean-field generalized contact process

Abstract

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