Abstract
We highlight some results from normal form theory for symmetric bifurcations that give a rational way to organize higher-order interactions between phase oscillators in networks with fully symmetric coupling. For systems near Hopf bifurcation the lowest order (pairwise) interactions correspond to the system of Kuramoto and Sakaguchi. At next asymptotic order one must generically include higher-order interactions of up to four oscillators. We discuss some dynamical consequences of these interactions in terms of heteroclinic attractors, chaos, and chimeras for related systems.
Original language | English |
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Title of host publication | Higher-Order Systems |
Editors | Federico Battiston, Giovanni Petri |
Place of Publication | Cham |
Publisher | Springer Science and Business Media Deutschland GmbH |
Pages | 197-216 |
Number of pages | 20 |
ISBN (Electronic) | 9783030913748 |
ISBN (Print) | 9783030913731 |
DOIs | |
Publication status | Published - 2022 |
Publication series
Name | Understanding Complex Systems (UCS) |
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Publisher | Springer |
ISSN (Print) | 1860-0832 |
ISSN (Electronic) | 1860-0840 |
Bibliographical note
Publisher Copyright:© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.