Abstract
The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble rather than time averages. The approach passes through the identification of locally stable and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy with generalized synchronization. The method is then applied to a periodically forced chaotic oscillator to show that the modulus of the Lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase synchronization. The analytical calculations are carried out for a model, the generalized special flow, that we construct as a simplified version of the periodically forced Rossler oscillator. (c) 2006 Elsevier BX All rights reserved.
Original language | English |
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Pages (from-to) | 90-101 |
Number of pages | 12 |
Journal | Physica. D, Nonlinear Phenomena |
Volume | 224 |
Issue number | 1-2 |
Early online date | 7 Nov 2006 |
DOIs | |
Publication status | Published - Dec 2006 |
Keywords
- synchronization
- Lyapunov exponents
- coupled chaotic oscillators
- phase synchronization
- transition
- systems
- modes