Hopf normal form with symmetry and reduction to systems of nonlinearly coupled phase oscillators
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- 作者：Peter Ashwin ; p.ashwin@exeter.ac.uk" class="auth_mail" title="E-mail the corresponding author ; Ana Rodrigues
- 关键词：Phase oscillator ; Hopf bifurcation ; Kuramoto ; Symmetry
- 刊名：Physica D: Nonlinear Phenomena
- 出版年：2016
- 出版时间：15 June 2016
- 年：2016
- 卷：325
- 期：Complete
- 页码：14-24
- 全文大小：1108 K
文摘
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We perform a phase reduction for weakly symmetrically interacting systems undergoing generic Hopf bifurcation.
For a low order truncation, we find interactions of up to four phases in addition to those of Kuramoto-type.
We find consequences of this on the bifurcation structure of two cluster states.