Abstract
We review some examples of dynamics displaying sequential switching for systems of coupled phase oscillators. As an illustration we discuss a simple family of coupled phase oscillators for which one can find robust heteroclinic networks between unstable cluster states. For N = 2 k+1 oscillators we show that there can be open regions in parameter space where the heteroclinic networks have the structure of an odd graph of order k; a class of graphs known from permutation theory. These networks lead to slow sequential switching between cluster states that is driven by noise and/or imperfections in the system. The dynamics observed is of relevance to modelling the emergent complex dynamical behaviour of coupled oscillator systems, e.g. for coupled chemical oscillators and neural networks.
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© 2010 Springer-Verlag Berlin Heidelberg
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Ashwin, P., Orosz, G., Borresen, J. (2010). Heteroclinic Switching in Coupled Oscillator Networks: Dynamics on Odd Graphs. In: Thiel, M., Kurths, J., Romano, M., Károlyi, G., Moura, A. (eds) Nonlinear Dynamics and Chaos: Advances and Perspectives. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04629-2_3
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DOI: https://doi.org/10.1007/978-3-642-04629-2_3
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04628-5
Online ISBN: 978-3-642-04629-2
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