Dynamic Responses of Networks under Perturbations: Solutions, Patterns and Predictions

by Xiaozhu Zhang
Doctoral thesis
Date of Examination:2018-01-11
Date of issue:2018-05-31
Advisor:Prof. Dr. Marc Timme
Referee:Prof. Dr. Marc Timme
Referee:Prof. Dr. Reiner Kree
Referee:Prof. Dr. Ulrich Parlitz
Persistent Address: http://dx.doi.org/10.53846/goediss-6898

 

 

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Abstract

English

External perturbations are omnipresent in the dynamics of oscillator networks across biology, physics and engineering. How such networks dynamically respond to fluctuating perturbation signals fundamentally underlies their function, yet is not well understood. In this thesis we investigate the dynamic responses of diffusively coupled oscillator networks to spatiotemporal perturbations close to a normal operation state. Employing methods such as linear response theory and asymptotic analysis, we discover a way to systematically link the second-order network dynamics to the network topology, thus obtain analytical insights into the patterns rising in the dynamic network responses. We study network response patterns in two timescales: (i) the long-term steady pattern driven by the external signals, and (ii) the short-term transient pattern in the spreading behaviour of a single signal. Based on the findings, we also propose practical schemes to accurately predict network responses in different timescales.
Keywords: oscillator networks; nonlinear dynamics; response patterns; perturbation spreading; power grids
 
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