Chimera states through invariant manifold theory
We establish the existence of chimera states, simultaneously supporting synchronous and asynchronous dynamics, in a network consisting of two symmetrically linked star subnetworks consisting of identical oscillators with shear and Kuramoto--Sakaguchi coupling. We show that the chimera states may be...
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| creator | Eldering, Jaap Lamb, Jeroen S W Pereira, Tiago Edmilson Roque dos Santos |
| description | We establish the existence of chimera states, simultaneously supporting synchronous and asynchronous dynamics, in a network consisting of two symmetrically linked star subnetworks consisting of identical oscillators with shear and Kuramoto--Sakaguchi coupling. We show that the chimera states may be metastable or asymptotically stable. If the intra-star coupling strength is of order \(\varepsilon\), the chimera states persist on time scales at least of order \(1/\varepsilon\) in general, and on time-scales at least of order \(1/\varepsilon^2\) if the intra-star coupling is of Kuramoto--Sakaguchi type. If the intra-star coupling configuration is sparse, the chimeras are asymptotically stable. The analysis relies on a combination of dimensional reduction using a M\"obius symmetry group and techniques from averaging theory and normal hyperbolicity. |
| doi_str_mv | 10.48550/arxiv.2102.04445 |
| format | Article |
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| subjects | Asymptotic properties Coupling Dimensional stability Mathematics - Dynamical Systems Oscillators Physics - Adaptation and Self-Organizing Systems |
| title | Chimera states through invariant manifold theory |
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