Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise

Journal article

We extend the theory of noise–induced phase synchronization to the case of a neural master equation describing the stochastic dynamics of interacting excitatory and inhibitory populations of neurons (E-I networks). The master equation formulation of stochastic neuro-dynamics represents the state of each population by the number of currently active neurons, and the state transitions are chosen such that deterministic Wilson–Cowan rate equations are recovered in the mean–field limit. Assuming that each deterministic E-I network acts as a limit cycle oscillator, we combine phase reduction and averaging methods in order to determine the stationary distribution of phase differences in an ensemble of uncoupled E-I oscillators, and use this to explore how intrinsic noise disrupts synchronization due to a common extrinsic noise source. 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 intrinsic noise leads to a stochastic hybrid system.

Authors: Bressloff, P; Lai, Y

• Publication date: 2010-01-01