TY - JOUR
T1 - Freak chimera states in a locally coupled Duffing oscillators chain
AU - Clerc, M. G.
AU - Coulibaly, S.
AU - Ferré, M. A.
N1 - Funding Information:
M.G.C. and M.A.F. are thankful for the financial support of CONICYT-USA, Project No. PII20150011 and Millenium Institute for Research in Optics (MIRO). M.G.C. thanks for the financial support FONDECYT project 1180903 . S.C. acknowledge the LABEX CEMPI (ANR-11-LABX-0007) as well as the Ministry of Higher Education and Research, Hauts de France council and European Regional Development Fund (ERDF) through the Contrat de Projets Etat-Region (CPER Photonics for Society P4S).
Publisher Copyright:
© 2020
PY - 2020/10/1
Y1 - 2020/10/1
N2 - Arrays of oscillators driven out-of-equilibrium can support the coexistence between coherent and incoherent domains that have become known as chimera states. Recently, we have reported such an intriguing self-organization phenomenon in a chain of locally coupled Duffing oscillators. Based on this prototype model, we reveal a generalization of chimera states corresponding to the coexistence of incoherent domains. These freak states emerge through a bifurcation in which the coherent domain of an existing chimera state experiences an instability giving rise to another incoherent state. Using Lyapunov exponents and Fourier analysis allows us to characterize the dynamical nature of these extended solutions. Taking the Kuramoto order parameter, we were able to compute the bifurcation diagram of freak chimera states.
AB - Arrays of oscillators driven out-of-equilibrium can support the coexistence between coherent and incoherent domains that have become known as chimera states. Recently, we have reported such an intriguing self-organization phenomenon in a chain of locally coupled Duffing oscillators. Based on this prototype model, we reveal a generalization of chimera states corresponding to the coexistence of incoherent domains. These freak states emerge through a bifurcation in which the coherent domain of an existing chimera state experiences an instability giving rise to another incoherent state. Using Lyapunov exponents and Fourier analysis allows us to characterize the dynamical nature of these extended solutions. Taking the Kuramoto order parameter, we were able to compute the bifurcation diagram of freak chimera states.
KW - Chimera states
KW - Coupled nonlinear oscillators
KW - Localized structures
UR - http://www.scopus.com/inward/record.url?scp=85083307570&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2020.105288
DO - 10.1016/j.cnsns.2020.105288
M3 - Article
AN - SCOPUS:85083307570
SN - 1007-5704
VL - 89
JO - Communications in Nonlinear Science and Numerical Simulation
JF - Communications in Nonlinear Science and Numerical Simulation
M1 - 105288
ER -