Dynamical Systems on Complex Networks

Alexander Joseph Khor

doi:10.26182/5c6f5d326e6b0

Dynamical Systems on Complex Networks

Alexander Joseph Khor

School of Physics, Mathematics and Computing

Research output: Thesis › Master's Thesis

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Abstract

This thesis examines the intersection of two popular fields of mathematics: dynamical systems and complex networks. We present two distinct cases of dynamical systems acting on complex networks, using the language of nonlinear science to highlight similarities between two problems usually studied separately within the disciplines of physics and computer science. Firstly, phase synchronisation, and in particular cluster synchronisation, is considered in the context of the Kuramoto model on a new model of complex networks. In the second section, we study consistency in echo state networks as a means of understanding the reservoir computing mechanism.

Original language	English
Qualification	Masters
Awarding Institution	The University of Western Australia
Supervisors/Advisors	Stemler, Thomas, Supervisor Small, Michael, Supervisor
Award date	29 Jan 2019
DOIs	https://doi.org/10.26182/5c6f5d326e6b0
Publication status	Unpublished - 2019

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10.26182/5c6f5d326e6b0

THESIS - MASTER OF PHILOSOPHY - KHOR Alexander Joseph - 2019
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Cite this

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AB - This thesis examines the intersection of two popular fields of mathematics: dynamical systems and complex networks. We present two distinct cases of dynamical systems acting on complex networks, using the language of nonlinear science to highlight similarities between two problems usually studied separately within the disciplines of physics and computer science. Firstly, phase synchronisation, and in particular cluster synchronisation, is considered in the context of the Kuramoto model on a new model of complex networks. In the second section, we study consistency in echo state networks as a means of understanding the reservoir computing mechanism.

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KW - Reservoir computing

KW - Generalised synchronisation

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