Motivated by our experimental observation that seizure activity in rat hippocampus can be modulated with an applied electric field (pictures), we use a network of model neurons coupled both synaptically and also through an external electric field to examine the role that this external electric field plays in the dynamical behavior of the neuronal ensembles. We have found that the electric field can be used as an effective parameter in modulating the synchrony among model neurons. We have found that although the boundary of synchrony as a function of both the electric field strength and the heterogeneity of the neurons can be quite complicated, the synchronization depends only on one intrinsic dynamical criterion - the natural frequency mismatch between the neurons. Most importantly, the phase locking state can be predicted from a phase reduction analysis.
Again, motivated by experiments (pictures), we are interested in examining the dynamics of wave propagations in an array of model neurons under the influence of an applied electric field. In a model of neurons arranged in a one dimensional array, the speed of a propagating spike wave can be modulated by an applied electric field as seen in experiments and other theoretical studies. With a sufficiently large suppressive field, spike waves can also be terminated. A bifurcation analysis of a single neuron model was shown to be useful in predicting these transitions. We are progressing in extending the analysis of this model with multi-neuron-types and we are also interested in examining the behavior of neural wave propagations in a medium with heterogeneous domains.