Sufficient Synchronization Conditions for Resistively and Memristively Coupled Oscillators of FitzHugh-Nagumo-type

We study the synchronization behavior of a class of identical FitzHugh-Nagumo-type oscillators under adaptive coupling. We describe the oscillators by a circuit model and we provide a sufficient synchronization condition that relies on the shape of the nonlinear conductance's $(i,u)$-curve and the connectivity of the adaptive coupling network. The coupling network is allowed to be time-variant, state-dependent and locally adaptive, where we treat memristive coupling elements as a special case. We provide a physical interpretation of synchronization in terms of power dissipation and investigate the sharpness of our condition.