Speaker:

Lachlan Smith, Postdoctoral Fellow, School of Mathematics and Statistics. The University of Sydney

Title:

Chaos in networks of coupled oscillators with multimodal natural frequency distributions

Abstract:

Synchronization is ubiquitous to networks of coupled oscillators. We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For multimodal natural frequency distributions it is typical that there is a range of coupling strengths such that multiple synchronized clusters coexist, with one synchronized cluster per peak in the frequency distribution. We use collective coordinates to describe the inter- and intra-cluster dynamics, which reduces the Kuramoto model to a small number of effective degrees of freedom. We show that chaos of the phases of clusters can occur provided there are at least four peaks in the frequency distribution, and that chaos can occur via intermittent desynchronization of a cluster if there are three peaks. In addition, we use collective coordinates to show analytically that chaos cannot occur for bimodal frequency distributions, even if they are asymmetric and if intermittent desynchronization occurs.

Speaker Bio:

Lachlan Smith is currently a Postdoctoral Fellow at the University of Sydney in the School of Mathematics and Statistics, working with Georg Gottwald. Lachlan is interested in the collective behaviour of dynamical entities in networks, such as the synchronization of coupled oscillators. He uses a collective coordinate approach to reduce the dimension of the model, which allows greater analytical insight. Before moving to Sydney, Lachlan was a Postdoctoral Fellow at Northwestern University, working with Julio Ottino, Richard Lueptow and Paul Umbanhowar to study mixing and transport by cutting-and-shuffling, with applications to granular mixing. Lachlan received his PhD from Monash University in Mechanical Engineering.

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