TY - JOUR
T1 - A Hopf bifurcation in the Kuramoto-Daido model
AU - Chiba, Hayato
N1 - Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2021/4/15
Y1 - 2021/4/15
N2 - A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency densities. The dynamical system of the order parameter on a four-dimensional center manifold is derived. It is shown that the dynamical system undergoes a Hopf bifurcation as the coupling strength increases, which proves the existence of a periodic two-cluster state of oscillators.
AB - A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency densities. The dynamical system of the order parameter on a four-dimensional center manifold is derived. It is shown that the dynamical system undergoes a Hopf bifurcation as the coupling strength increases, which proves the existence of a periodic two-cluster state of oscillators.
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U2 - 10.1016/j.jde.2021.01.024
DO - 10.1016/j.jde.2021.01.024
M3 - Article
AN - SCOPUS:85100318663
SN - 0022-0396
VL - 280
SP - 546
EP - 570
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -