WIAS Preprint No. 788, (2002)

Identical synchronization of time-continuous chaotic oscillators



Authors

  • Yanchuk, Serhiy
  • Maistrenko, Yuri
  • Mosekilde, Erik

2010 Mathematics Subject Classification

  • 34C15 34D05 34D20

Keywords

  • chaotic synchronization, coupled oscillators, Roessler oscillators

Abstract

Considering a system of two coupled identical chaotic oscillators, the paper first establishes the conditions of transverse stability for the fully synchronized chaotic state. Periodic orbit threshold theory is applied to determine the bifurcations through which low-periodic orbits embedded in the fully synchronized state lose their transverse stability, and the appearance of globally and locally riddled basins of attraction is discussed in terms of the sub-, respectively supercritical nature of the riddling bifurcations. We show how the introduction of a small parameter mismatch between the interacting chaotic oscillators causes a shift of the synchronization manifold. The presence of a coupling asymmetry is found to lead to further modifications of the destabilization process. Finally, the paper considers the problem of partial synchronization in a system of four coupled Rössler oscillators.

Appeared in

  • Chaos, 13 (2003), pp. 388-400

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