Emergence of bursting in two coupled neurons of different types of excitability

In this manuscript, a spiking neuron of type I excitability and a silent neuron of type II excitability are coupled through a gap junction with unequal coupling strengths, and none of the coupled neurons can burst intrinsically. By applying the theory of dynamical systems (e.g. bifurcation theory), we investigate how the coupling strength affects the dynamics of the neurons, when one of the coupling strengths is fixed and the other varies. We report four different regimes of oscillations as the coupling strength increases. (1) Spike–Spike Phase–Locking, where both neurons are in tonic spiking mode but with different frequencies; (2) Spike–Burst mode, where the type II neuron bursts while the type I neuron remains in tonic spiking mode; (3) Burst–Burst synchronization, where the neurons burst synchronously, i.e., both neurons enter and exit the active phase almost together; (4) Spike–Spike Synchronization, where the neurons synchronize as two oscillators, i.e., they oscillate with equal time period and fraquency. An interesting finding is that there exist two different synchronous behaviours, one of them corresponds to 1−burst synchronization of the neurons and the other corresponds to the synchronizations of 1−bursting oscillations in type II neuron and tonic spiking oscillations in type I neuron. Finally it should be pointed out that all through increasing the coupling strength we observe sequences of intermittency in the neurons, which is an abrupt and irregular transition between periodic oscillations and chaotic dynamics.