Desynchronization transitions in adaptive networks

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.

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• Co-evolutionary dynamics for two adaptively coupled Theta neurons
• Recurrent chaotic clustering and slow chaos in adaptive networks
• Complex Couplings -- A universal, adaptive and bilinear formulation of power grid dynamics
• Collective excitability in highly diluted networks of rotators
• Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics
• Mean field limits of co-evolutionary signed heterogeneous networks
• Modelling power grids as pseudo adaptive networks