It is a fundamental challenge to understand how the function of a network is related to its
structural organization. Adaptive dynamical networks represent a broad class of systems that …

Phase transitions in equilibrium and nonequilibrium systems play a major role in the natural
sciences. In dynamical networks, phase transitions organize qualitative changes in the …

We prove the existence of a multidimensional nontrivial invariant toroidal manifold for the
Kuramoto network with adaptive coupling. The constructed invariant manifold corresponds …

Cluster synchronization is of great importance for the normal functioning of numerous
technological and natural systems. Deviations from normal cluster synchronization patterns …

Cluster synchronization underlies various functions in the brain. Abnormal patterns of cluster
synchronization are often associated with neurological disorders. Deep brain stimulation …

The Kuramoto model is a classical model used for the describing of synchronization in
populations of oscillatory units. In the present paper we study the Kuramoto model with …

This chapter addresses the problems of synchronization analysis in various types of
oscillator networks. In particular, we derive sufficient conditions for emergence of multi …