Abstract
We extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. The master equation formulation of stochastic neurodynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen so that deterministic Wilson-Cowan rate equations are recovered in the mean-field limit. We apply phase reduction and averaging methods to a corresponding Langevin approximation of the master equation in order to determine how intrinsic noise disrupts synchronization of the population oscillators driven by a common extrinsic noise source. We illustrate our analysis by considering one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I) subpopulations. We show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of the population oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. Finally, we show how a similar analysis can be carried out for another simple population model that exhibits limit cycle oscillations in the deterministic limit, namely, a recurrent excitatory network with synaptic depression; inclusion of synaptic depression into the neural master equation now generates a stochastic hybrid system.
Highlights
Synchronous oscillations are prevalent in many areas of the brain including sensory cortices, thalamus and hippocampus [1]
In the case of an E-I network, we show how the combination of intrinsic independent noise and extrinsic common noise can lead to clustering of limit cycle oscillators due to the multiplicative nature of both noise sources under the Langevin approximation. (Clustering would not occur in the case of additive noise.) we show how a similar analysis can be carried out for another important neuronal population model that exhibits limit cycle oscillations in the deterministic limit, namely, an excitatory recurrent network with synaptic depression; such a network forms the basis of various studies of spontaneous synchronous oscillations in cortex [39,40,41,42,43]
In this paper we extended the theory of noise-induced synchronization to a stochastic Wilson-Cowan model of neural population dynamics formulated as a neural master equation
Summary
Synchronous oscillations are prevalent in many areas of the brain including sensory cortices, thalamus and hippocampus [1]. In this paper we extend the theory of noise-induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of an ensemble of uncoupled neuronal population oscillators with intrinsic and extrinsic noise. We apply stochastic phase reduction and averaging methods to the corresponding system of neural Langevin equations, following along similar lines to Nakao et al [12], and use this to determine how independent intrinsic noise disrupts synchronization due to a common extrinsic noise source. We consider a stochastic population model in which the independent noise sources are due to finite size effects intrinsic to each oscillator.) We apply our analysis to one of the simplest networks known to generate limit cycle oscillations at the population level, namely, a pair of mutually coupled excitatory (E) and inhibitory (I ) subpopulations [36]. We highlight how the inclusion of synaptic depression into the master equation formulation leads to a novel example of a stochastic hybrid system [44]
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call