Phase chaos in coupled oscillators

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Phase chaos in coupled oscillators

Oleksandr V. Popovych, Yuri L. Maistrenko, and Peter A. Tass

Phys. Rev. E 71, 065201(R) – Published 6 June 2005

Abstract

A complex high-dimensional chaotic behavior, phase chaos, is found in the finite-dimensional Kuramoto model of coupled phase oscillators. This type of chaos is characterized by half of the spectrum of Lyapunov exponents being positive and the Lyapunov dimension equaling almost the total system dimension. Intriguingly, the strongest phase chaos occurs for intermediate-size ensembles. Phase chaos is a common property of networks of oscillators of very different natures, such as phase oscillators, limit-cycle oscillators, and chaotic oscillators, e.g., Rössler systems.

Received 1 December 2004

DOI:https://doi.org/10.1103/PhysRevE.71.065201

Authors & Affiliations

Oleksandr V. Popovych¹, Yuri L. Maistrenko^1,2,3, and Peter A. Tass^1,4

¹Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre Jülich, 52425 Jülich, Germany
²Central Institute for Electronics, Research Center Jülich, 52425 Jülich, Germany
³Institute of Mathematics, National Academy of Sciences of Ukraine, 01601 Kyiv, Ukraine
⁴Department of Stereotaxic and Functional Neurosurgery, University Hospital, 50924 Cologne, Germany

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Issue

Vol. 71, Iss. 6 — June 2005

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