Bifurcations in modified BVP neurons connected by inhibitory and electrical coupling

Electrical coupling among inhibitory interneurons has been discovered in various regions of the brain. Since these local networks indicate a sophisticated activity by the interplay between electrical and inhibitory synapses, the emergence of synchronous phenomena have been investigated by many researchers. We propose coupled neuronal models connected by both inhibitory and electrical synapses and investigate the emergence of various synchronous phenomena and its bifurcational structures by bifurcation analysis. Although it is generally known that a strong gap junction synchronizes coupled neurons, we show in-phase and anti-phase phenomena in coupled neurons connected by both inhibitory and electrical synapses. They change to chaotic solutions via period-doubling and pitchfork bifurcations.