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The focus of this thesis are synchronization phenomena in networks
and their intrinsic control through time delay, which is ubiquitous
in real-world systems ranging from physics and acoustics to
neuroscience and engineering. We encounter synchronization
everywhere and it can be either a helpful or a detrimental
mechanism. In the first part, after a survey of complex nonlinear
systems and networks, we show that a seemingly simple system of two
organ pipes gives birth to complex bifurcation and synchronization
scenarios. Going from a 2-oscillator system to a ring of
oscillators, we encounter the intriguing phenomenon of chimera
states which are partial synchrony patterns with coexisting domains
of synchronized and desynchronized dynamics. For more than a decade
scientist have tried to solve the puzzle of this spontaneous
symmetry-breaking emerging in networks of identical elements. We
provide an analysis of initial conditions and extend our model by
the addition of time delay and fractal connectivities. In the
second part, we investigate partial synchronization patterns in a
neuronal network and explain dynamical asymmetry arising from the
hemispheric structure of the human brain. A particular focus is on
the novel scenario of partial relay synchronization in multiplex
networks. Such networks allow for synchronization of the coherent
domains of chimera states via a remote layer, whereas the
incoherent domains remain desynchronized. The theoretical framework
is demonstrated with different generic models.
The focus of this thesis are synchronization phenomena in networks
and their intrinsic control through time delay, which is ubiquitous
in real-world systems ranging from physics and acoustics to
neuroscience and engineering. We encounter synchronization
everywhere and it can be either a helpful or a detrimental
mechanism. In the first part, after a survey of complex nonlinear
systems and networks, we show that a seemingly simple system of two
organ pipes gives birth to complex bifurcation and synchronization
scenarios. Going from a 2-oscillator system to a ring of
oscillators, we encounter the intriguing phenomenon of chimera
states which are partial synchrony patterns with coexisting domains
of synchronized and desynchronized dynamics. For more than a decade
scientist have tried to solve the puzzle of this spontaneous
symmetry-breaking emerging in networks of identical elements. We
provide an analysis of initial conditions and extend our model by
the addition of time delay and fractal connectivities. In the
second part, we investigate partial synchronization patterns in a
neuronal network and explain dynamical asymmetry arising from the
hemispheric structure of the human brain. A particular focus is on
the novel scenario of partial relay synchronization in multiplex
networks. Such networks allow for synchronization of the coherent
domains of chimera states via a remote layer, whereas the
incoherent domains remain desynchronized. The theoretical framework
is demonstrated with different generic models.
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