We show that firing activity (spiking) can be regularized by noise in a FitzHugh-Nagumo (FHN) neuron model when operating slightly beyond the supercritical Hopf bifurcation (in the "canard" region). We also provide the conditions for imperfect phase locking between interspike intervals and low amplitude quasiharmonic oscillations. For the imperfect phase locking no need exists of an external si...

Can we express biophysical neuronal models as integrate-and-fire (IF) models with leakage coefficients which are no longer constant, as in the conventional leaky IF model, but functions of membrane potential and other biophysical variables? We illustrate the answer to this question using the FitzHugh-Nagumo (FHN) model as an example. A novel IF type model, the IF-FHN model, which approximates t...

We examine a generalized FitzHugh-Nagumo (FHN) type model with modified excitability derived from the diffusive Morris-Lecar equations for neuronal activity. We obtain exact analytic solutions in the form of traveling waves using a piecewise linear approximation for the activator and inhibitor reaction terms. We study the existence and stability of waves and find that the inhibitor species exhi...

He received his B.Sc. degree in Biology (1990) from Department of Biology, University of British Columbia, Canada, also M.Sc. in Botany (1993) from Department of Botany, University of British Columbia, Canada and Ph.D. in Plant Ecology (1996) from Department of Animal & Plant Sciences, University of Sheffield, England.Dr. Fraser's expertise is in grassland and wetland ecosystems, with a focus o...