Destabilization patterns in large regular networks

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Date
2007
Volume
1213
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Journal
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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract

We describe a generic mechanism for the destabilization in large regular networks of identical coupled oscillators. Based on a reduction method for the spectral problem, we first present a criterion for this type of destabilization. Then, we investigate the related bifurcation scenario, showing the existence of a large number of coexisting periodic solutions with different frequencies, spatial patterns, and stability properties. Even for unidirectional coupling this can be understood in analogy to the well-known Eckhaus scenario for diffusive systems.

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Yanchuk, S., & Wolfrum, M. (2007). Destabilization patterns in large regular networks (Vol. 1213). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.
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