My research in neural dynamics tries to advance the understanding of the nervous system through modeling of interactions of populations of neurons using ideas from stochastic dynamics. Interactions of excitatory and inhibitory populations produce oscillations which are sustained by noise. Analysis of a corresponding stochastic process yields information about pattern of firing.
The dynamics of cortex, in the absence of external input, may be modeled as an evolving random field. With Lawrence Ward (Psychology, UBC) we explore the interaction of spatial and temporal fluctuations formed by systems of stochastic reaction-coupling equations.
Other areas of continuing interest are:
statistics of stochastic processes,
stochastic models in epidemiology, population dynamics,
the ubiquitous phenomenon of data which have a spectral density function similar to inverse frequency for several decades of frequency.