Burst mechanisms and burst synchronization in a system of coupled type-I and type-II neurons

The rich dynamics of a system comprising of a Type-I neuron coupled to a Type-II neuron via an electrical synapse (gap junction) are explored in this paper. Diverse dynamical behaviour ranging from quiescence and periodic spiking, to bursting and burst synchronization, were observed for different coupling schemes. The bifurcation mechanisms underlying the various bursts observed were identified. We report a unique burst mechanism, based on a focus/node bifurcation, occurring for bidirectionally coupled neurons. We attempt to understand the physical basis for the transitions from one burst pattern to another and also between the different aforementioned forms of dynamical behaviour observed on varying the coupling strength, in both unidirectionally and bidirectionally coupled neurons. The various dynamical regimes of the coupled system are exhaustively studied and demarcated through parameter plots. Type-I and type-II neurons exhibit mutually phase synchronized burst patterns at large values of the coupling which tend towards complete synchronization on increasing the coupling strength. Such collective dynamical behaviour can have important implications in biological systems