Chimera states through invariant manifold theory. (English) Zbl 07368123

Y. Kuramoto and D. Battogtokh [Nonlinear Phenom. Complex Syst., 5, No. 4, 380–385 (2002)] observed the coexistence of synchronous and asynchronous oscillations in a ring of identical coupled oscillators. This phenomenon of partial synchronization in networks of identical coupled oscillators is known as “chimera” and it is observed in a wide range of experimental settings.
In this paper the authors obtain some mathematical results on the chimera behavior in a large but finite size network of identical oscillators, with a specific modular structure and a relatively general type of coupling. A simple example is the union of two identical, symmetrically coupled star subnetworks. The key ingredients that underlie the analysis are a dimensional reduction due to a Möbius group symmetry, averaging theory and normally hyperbolic invariant manifold theory.


37D10 Invariant manifold theory for dynamical systems
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
34C29 Averaging method for ordinary differential equations
34D06 Synchronization of solutions to ordinary differential equations
34C45 Invariant manifolds for ordinary differential equations
70K50 Bifurcations and instability for nonlinear problems in mechanics


Full Text: DOI arXiv


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