Title
Cascades of multiheaded chimera states for coupled phase oscillators Cascades of multiheaded chimera states for coupled phase oscillators
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
Singapore ,
Subject
Mathematics
Engineering sciences. Technology
Source (journal)
International journal of bifurcation and chaos in applied sciences and engineering. - Singapore
Volume/pages
24(2014) :8 , 17 p.
ISSN
0218-1274
0218-1274
Article Reference
1440014
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.
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