Journal
PHYSICAL REVIEW E
Volume 82, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.82.051903
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Funding
- National Science Foundation [DMS-0813677]
- King Abdullah University of Science and Technology (KAUST) [KUK-C1-013-4]
- Royal Society Wolfson Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0813677] Funding Source: National Science Foundation
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We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N ->infinity, where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N, we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers-Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles).
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