5,051 research outputs found
Control of coupled oscillator networks with application to microgrid technologies
The control of complex systems and network-coupled dynamical systems is a
topic of vital theoretical importance in mathematics and physics with a wide
range of applications in engineering and various other sciences. Motivated by
recent research into smart grid technologies we study here control of
synchronization and consider the important case of networks of coupled phase
oscillators with nonlinear interactions--a paradigmatic example that has guided
our understanding of self-organization for decades. We develop a method for
control based on identifying and stabilizing problematic oscillators, resulting
in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized
state. Interestingly, the amount of control, i.e., number of oscillators,
required to stabilize the network is primarily dictated by the coupling
strength, dynamical heterogeneity, and mean degree of the network, and depends
little on the structural heterogeneity of the network itself
Optimal global synchronization of partially forced Kuramoto oscillators
We consider the problem of global synchronization in a large random network
of Kuramoto oscillators where some of them are subject to an external
periodically driven force. We explore a recently proposed dimensional reduction
approach and introduce an effective two-dimensional description for the
problem. From the dimensionally reduced model, we obtain analytical predictions
for some critical parameters necessary for the onset of a globally synchronized
state in the system. Moreover, the low dimensional model also allows us to
introduce an optimization scheme for the problem. Our main conclusion, which
has been corroborated by exhaustive numerical simulations, is that for a given
large random network of Kuramoto oscillators, with random natural frequencies
, such that a fraction of them is subject to an external periodic
force with frequency , the best global synchronization properties
correspond to the case where the fraction of the forced oscillators is chosen
to be those ones such that is maximal. Our results might
shed some light on the structure and evolution of natural systems for which the
presence or the absence of global synchronization are desired properties. Some
properties of the optimal forced networks and its relation to recent results in
the literature are also discussed.Comment: 8 pages, 3 figures. Final version accepted for publication in Chaos.
After it is published, it will be found at
https://publishing.aip.org/resources/librarians/products/journals
Synchronization is optimal in non-diagonalizable networks
We consider the problem of maximizing the synchronizability of oscillator
networks by assigning weights and directions to the links of a given
interaction topology. We first extend the well-known master stability formalism
to the case of non-diagonalizable networks. We then show that, unless some
oscillator is connected to all the others, networks of maximum
synchronizability are necessarily non-diagonalizable and can always be obtained
by imposing unidirectional information flow with normalized input strengths.
The extension makes the formalism applicable to all possible network
structures, while the maximization results provide insights into hierarchical
structures observed in complex networks in which synchronization plays a
significant role.Comment: 4 pages, 1 figure; minor revisio
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