Dynamics on graphs and dynamics of graphs in coupled oscillator systems of small, medium and large sizes

Benjamin Jüttner

Research output: Book/ReportPh.D. thesis

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Abstract

We investigate the dynamics of N coupled oscillators on (adaptive) graphs. To make progress on the question how synchronization depends on the graph structure or on how much the graph can adapt, we carry out three studies. Firstly, we study a symmetric system of two populations of nonidentical inhibitory Theta neurons in the N → ∞ limit and investigate the dynamics depending on the inter- and the intra-population coupling. Secondly, we study the stochastic Kuramoto model on graphops (generalized graphs of infinite size), give a critical coupling strength for the onset of partial coherence, and complement this analytical result with numerical experiments on different (finite) graphs. Finally, we study an adaptive Kuramoto model on (un)directed graphs, mainly for N = 2 and partly for N = 50 oscillators. Although the most complex dynamical behaviour in our studies requires the graph to be directed and adaptive, complicated behaviour can already occur for perfectly symmetric, nonadaptive systems. Moreover, strong irregularities or a relatively low number of edges can weaken the graph's ability to synchronize the oscillators.
Original languageEnglish
PublisherTechnical University of Denmark
Number of pages120
Publication statusPublished - 2022

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