Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise

 We examine several aspects of introducing stochasticity into dynamical systems, with specific applications to modelling
populations of neurons. In particular, we use the example of a interacting
populations of excitatory and inhibitory neurons (E-I networks). As each
network consists of a large but finite number of neurons that fire
stochastically, we can study the effect of this intrinsic noise using a master
equation formulation. In the parameter regime where each E-I network acts as a
limit cycle oscillator, we combine phase reduction and averaging to study the
stationary distribution of phase differences in an ensemble of uncoupled E-I
oscillators, and explore how the intrinsic noise disrupts synchronization due
to a common external noise source.