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Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators (Hardcover, 1st ed. 2021)
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Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators (Hardcover, 1st ed. 2021)
Series: Springer Theses
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The focus of this thesis is the interplay of synchrony and
adaptivity in complex networks. Synchronization is a ubiquitous
phenomenon observed in different contexts in physics, chemistry,
biology, neuroscience, medicine, socioeconomic systems, and
engineering. Most prominently, synchronization takes place in the
brain, where it is associated with cognitive capacities like
learning and memory, but is also a characteristic of neurological
diseases like Parkinson and epilepsy. Adaptivity is common in many
networks in nature and technology, where the connectivity changes
in time, i.e., the strength of the coupling is continuously
adjusted depending upon the dynamic state of the system, for
instance synaptic neuronal plasticity in the brain. This research
contributes to a fundamental understanding of various
synchronization patterns, including hierarchical multifrequency
clusters, chimeras and other partial synchronization states. After
a concise survey of the fundamentals of adaptive and complex
dynamical networks and synaptic plasticity, in the first part of
the thesis the existence and stability of cluster synchronization
in globally coupled adaptive networks is discussed for simple
paradigmatic phase oscillators as well as for a more realistic
neuronal oscillator model with spike-timing dependent plasticity.
In the second part of the thesis the interplay of adaptivity and
connectivity is investigated for more complex network structures
like nonlocally coupled rings, random networks, and multilayer
systems. Besides presenting a plethora of novel, sometimes
intriguing patterns of synchrony, the thesis makes a number of
pioneering methodological advances, where rigorous mathematical
proofs are given in the Appendices. These results are of interest
not only from a fundamental point of view, but also with respect to
challenging applications in neuroscience and technological systems.
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