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

Partial, instead of complete, synchronization has been widely observed in various networks,
including, in particular, brain networks. Motivated by data from human brain functional …

In this paper, we propose a framework to control brain-wide functional connectivity by
selectively acting on the brain's structure and parameters. Functional connectivity, which …

Remote synchronization describes a fascinating phenomenon where oscillators that are not
directly connected via physical links evolve synchronously. This phenomenon is thought to …

New stability conditions for cluster synchronization of Kuramoto oscillators are presented.
Our approach is based on averaging criteria, but the standard method for stability analysis …

This paper studies stability properties of multi-cluster formations in Kuramoto networks with
adaptive coupling. Sufficient conditions for the local asymptotic stability of the corresponding …

Feedback linearization allows for the local transformation of a nonlinear system to an
equivalent linear one by means of a coordinate transformation and a feedback law …

Partial, instead of complete, synchronization has been widely observed in various networks
including, in particular, brain networks. Motivated by data from human brain functional …

Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The
method of averaging plays an important role in stability analysis, but the standard …

Reverse engineering the brain holds the promise to overhaul the quality of life of human
beings and vastly benefit mankind. Further advances towards this goal will lead to the …