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Abstract:
Adaptive networks change their connectivity with time, depending on their dynamical state.
While synchronization in structurally static networks has been studied extensively, this problem
is much more challenging for adaptive networks. In this Letter, we develop the master stability
approach for a large class of adaptive networks. This approach allows for reducing the synchronization
problem for adaptive networks to a low-dimensional system, by decoupling topological and
dynamical properties. We show how the interplay between adaptivity and network structure gives
rise to the formation of stability islands. Moreover, we report a desynchronization transition and
the emergence of complex partial synchronization patterns induced by an increasing overall coupling
strength. We illustrate our findings using adaptive networks of coupled phase oscillators and
FitzHugh-Nagumo neurons with synaptic plasticity.
