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Synchronization is critical for system function in applications ranging from cardiac pacemakers to power grids. Existing optimization techniques rely largely on global information, and while they induce certain local properties, those alone do not yield optimal systems. Therefore, while useful for designing man-made systems, existing theory provides limited insight into self-optimization of naturally-occurring systems that rely on local information and offer limited potential for decentralized optimization. Here we present a method for grass-roots optimization of synchronization, which is a multiscale mechanism involving local optimizations of smaller subsystems that are coordinated to collectively optimize an entire system, and the dynamics of such systems are particularly robust to islanding or targeted attacks. In addition to shedding light on self-optimization in natural systems, grass-roots optimization can also support the parallelizable and scalable engineering of man-made systems.
The behavior at bifurcation from global synchronization to partial synchronization in finite networks of coupled oscillators is a complex phenomenon, involving the intricate dynamics of one or more oscillators with the remaining synchronized oscillat
We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of
The Kuramoto model, which serves as a paradigm for investigating synchronization phenomenon of oscillatory system, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here, we generalize a number
A scenario has recently been reported in which in order to stabilize complete synchronization of an oscillator network---a symmetric state---the symmetry of the system itself has to be broken by making the oscillators nonidentical. But how often does
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows throughout the grid