From synchronization to Lyapunov exponents and back

被引:17
|
作者
Politi, Antonio
Ginelli, Francesco
Yanchuk, Serhiy
Maistrenko, Yuri
机构
[1] CNR, Ist Sist Complessi, I-50019 Sesto Fiorentino, Italy
[2] CEA Saclay, Serv Phys & Etat Condense, F-91191 Gif Sur Yvette, France
[3] Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev, Ukraine
[4] Weierstrass Inst Appl Anal & Stochast, D-10117 Berlin, Germany
[5] Humboldt Univ, Math Inst, D-10099 Berlin, Germany
[6] Res Ctr Julich, Inst Med & Virtual Inst Neuromodulat, D-52425 Julich, Germany
关键词
synchronization; Lyapunov exponents;
D O I
10.1016/j.physd.2006.09.032
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:90 / 101
页数:12
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