Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-05-03
Physica D 224, 90 (2006).
Nonlinear Sciences
Chaotic Dynamics
Submitted to Physica D
Scientific paper
10.1016/j.physd.2006.09.032
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.
Ginelli Francesco
Maistrenko Yuri
Politi Antonio
Yanchuk Serhiy
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