We consider networks of quadratic integrate-and-fire neurons coupled via
both chemical synapses and gap junctions. After transforming to “theta neuron” coordinates,
a network’s governing equations are of a form amenable to the use of the
Ott/Antonsen ansatz. This ansatz allows us to derive an exact description of a network’s
dynamics in the limit of an infinite number of neurons. For an all-to-all connected
network we derive a single (complex) ordinary differential equation while for
spatially extended networks we derive neural field equations (nonlocal partial differential
equations). We perform extensive numerical analysis of the resulting equations,
showing how the presence of gap junctional coupling can destroy certain spatiotemporal
patterns such as stationary “bump” solutions and create others such as travelling
waves and spatiotemporal chaos. Our results provide significant insight into the effects
of gap junctions on the dynamics of networks of Type I neurons.
| Author Institutional Affiliation | Massey University, Auckland, New Zealand |
| Author Email | |
| Author Postal Mail | Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand |
| Notes | |
| Keywords | neural field, quadratic integrate-and-fire, gap junction, Ott/Antonsen, bifurcation, theta neuron |