Two Coupled Neurons

We review the dynamical behaviour of a system of two coupled neurons. We consider symmetric and asymmetric linear coupling. The internal dynamics of each neuron is modeled by the space-clamped Hodgkin-Huxley equations. We start with the symmetric case. Results in the literature show that for strong enough coupling the two neurons show the same behaviour at all times. They may be periodically spiking or at rest. We define these states as perfect synchrony. When decreasing the coupling strength to small positive values almost perfect synchronization is retained. As we move towards negative values of the coupling the two neurons still synchronize but in a different way, they spike periodically with half-period phase shift from each other. As we go towards lower negative values, the system becomes totally unstable. Periodic states where the two neurons synchronize are also defined as 1:1 phase locked modes. The asymmetric coupled system is studied as a perturbation from the symmetric case.