6,963 research outputs found
Synchronization of heterogeneous oscillators under network modifications: Perturbation and optimization of the synchrony alignment function
Synchronization is central to many complex systems in engineering physics
(e.g., the power-grid, Josephson junction circuits, and electro-chemical
oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms).
Despite these widespread applications---for which proper functionality depends
sensitively on the extent of synchronization---there remains a lack of
understanding for how systems evolve and adapt to enhance or inhibit
synchronization. We study how network modifications affect the synchronization
properties of network-coupled dynamical systems that have heterogeneous node
dynamics (e.g., phase oscillators with non-identical frequencies), which is
often the case for real-world systems. Our approach relies on a synchrony
alignment function (SAF) that quantifies the interplay between heterogeneity of
the network and of the oscillators and provides an objective measure for a
system's ability to synchronize. We conduct a spectral perturbation analysis of
the SAF for structural network modifications including the addition and removal
of edges, which subsequently ranks the edges according to their importance to
synchronization. Based on this analysis, we develop gradient-descent algorithms
to efficiently solve optimization problems that aim to maximize phase
synchronization via network modifications. We support these and other results
with numerical experiments.Comment: 25 pages, 6 figure
Transient Uncoupling Induces Synchronization
Finding conditions that support synchronization is a fertile and active area
of research with applications across multiple disciplines. Here we present and
analyze a scheme for synchronizing chaotic dynamical systems by transiently
uncoupling them. Specifically, systems coupled only in a fraction of their
state space may synchronize even if fully coupled they do not. Although, for
many standard systems, coupling strengths need to be bounded to ensure
synchrony, transient uncoupling removes this bound and thus enables
synchronization in an infinite range of effective coupling strengths. The
presented coupling scheme thus opens up the possibility to induce synchrony in
(biological or technical) systems whose parameters are fixed and cannot be
modified continuously.Comment: 5 pages, 6 figure
- …