Limits to detection of generalized synchronization in delay-coupled chaotic oscillators.
We study how reliably generalized synchronization can be detected and characterized from time-series analysis. To that end, we analyze synchronization in a generalized sense of delay-coupled chaotic oscillators in unidirectional ring configurations. The generalized synchronization condition can be verified via the auxiliary system approach; however, in practice, this might not always be possible. Therefore, in this study, widely used indicators to directly quantify generalized and phase synchronization from noise-free time series of two oscillators are employed complementarily to the auxiliary system approach. In our analysis, none of the indices provide the consistent results of the auxiliary system approach. Our findings indicate that it is a major challenge to directly detect synchronization in a generalized sense between two oscillators that are connected via a chain of other oscillators, even if the oscillators are identical. This has major consequences for the interpretation of the dynamics of coupled systems and applications thereof.
Center for Simulation Sciences, Ochanomizu University, 2-1-1 Ohtsuka Bunkyo-ku, 112-8610 Tokyo, Japan.
Hideyuki
H
Kato
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC, (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
Miguel C
MC
Soriano
Departamento de Física Básica, ETS de Ing. Civil e Industrial, Universidad de La Laguna Avda. Astrofísico Fco. Sánchez, s/n, 38205, La Laguna, Tenerife, Spain.
Ernesto
E
Pereda
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC, (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
Ingo
I
Fischer
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC, (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain.
Claudio R
CR
Mirasso