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Phase response curves and emergent dynamics in oscillator networks

Prof. Peter Ashwin, PhD:


It is well known that coupled dynamical systems can self-organize into a variety of synchronized or partially synchronized states via the emergent dynamics of their interaction. Clearly the topology of the interactions and their strengths are important for what emerges. This talk will examine the influence not only of the topology and strength of the coupling but also of the exact functional form of the phase response curve for phase oscillator networks. For these networks a lot can be understood using analytical tools from symmetric dynamics. In the case of all-to-all coupled networks, clustered attracting and repelling behaviour can be characterised in terms of local properties of a phase response curve - there can exist arbitrarily complex clustered attractors for appropriate choice of phase response curve. In addition to these dynamically simple attractors there can be a wide range of chaotic and/or heteroclinic network attractors in such systems. This talk will review some examples of these as well as highlighting some open problems in this area.

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