7. Strongly coupled spiking networks

In Chap. 6, we explored how collective behaviour, such as synchronous network oscillations and phase waves, are generated in weakly coupled networks. For networks of spiking networks, the assumption of weak interactions allows us to reduce the full network model down to one that describes each neuron by its phase along an underlying spiking orbit. In this way, the dynamics for the system are considered only on a reduced phase space given by the Cartesian product of each neuron’s periodic orbit. Whilst the individual postsynaptic currents induced by spiking events may be small, their sum over time (since these currents have a characteristic decay timescale) and over the set of pre-synaptic neurons to which a given cell is coupled, may not be. In addition, the phase reduction approach can only be used when the uncoupled dynamics of each neuron is oscillatory. Hence, the weakly coupled framework is unable to describe networks of excitable cells. In this chapter, we relax the assumption of weak coupling and present results for collective dynamics in networks with arbitrary coupling strength. It is important to stress that we currently lack a general theory for strongly coupled networks and that results presented here are mostly for specific model choices.