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arXiv · 2102.04445

Chimera states through invariant manifold theory

Jaap Eldering·Jeroen S. W. Lamb·Tiago Pereira·Edmilson Roque dos Santos
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Abstract

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.

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Jaap Eldering, Jeroen S. W. Lamb, Tiago Pereira, Edmilson Roque dos Santos. 2021-02-08. Chimera states through invariant manifold theory. https://doi.org/10.1088/1361-6544/ac0613

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