Strongly asymmetric clustering in systems of phase oscillators.
In this paper, we look at clustering in systems of globally coupled identical phase oscillators. In particular, we extend and apply techniques developed earlier to study stable clustering behavior involving clusters of greatly differing size. We discuss the bifurcations in which these asymmetric cluster states are created, and how these relate to bifurcations of the synchronized state. Because of the simplicity of systems of phase oscillators, it is possible to say a significant amount about asymmetric clustering analytically. We apply some of the theory developed to one particular system, and illustrate how the techniques can be used to find behavior which might otherwise be missed.
Banaji
Murad
M
Department of Medical Physics and Bioengineering, University College London, Malet Place Engineering Building, Gower Street, London WC1E 6BT, United Kingdom.