Amplitude equations and fast transition to chaos in rings of coupled oscillators - Mathematics > Dynamical SystemsReportar como inadecuado




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Abstract: We study the coupling induced destabilization in an array of identicaloscillators coupled in a ring structure where the number of oscillators in thering is large. The coupling structure includes different types of interactionswith several next neighbors. We derive an amplitude equation of Ginzburg-Landautype, which describes the destabilization of a uniform stationary state in aring with a large number of nodes. Applying these results to unidirectionallycoupled Duffing oscillators, we explain the phenomenon of a fast transition tochaos, which has been numerically observed in such systems. More specifically,the transition to chaos occurs on an interval of a generic control parameterthat scales as the inverse square of the size of the ring, i.e. forsufficiently large system, we observe practically an immediate transition tochaos.



Autor: S. Yanchuk, P. Perlikowski, M. Wolfrum, A. Stefanski, T. Kapitaniak

Fuente: https://arxiv.org/







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