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