Detecting Generalized Synchronization Between Chaotic Signals: A Kernel-based Approach
arXiv:nlin/0507006 · doi:10.1088/0305-4470/39/34/009
Abstract
A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several successful applications are presented, which show the capability of the kernel-based approach for detecting generalized synchronization. It is also shown that the dynamical change of the coupling coefficient between two chaotic systems can be captured by the proposed approach.
arXiv comment20 pages, 15 figures. massively revised as a full paper; issues on the choice of parameters by cross validation, tests by surrogated data, etc. are added as well as additional examples and figures
References in corpus (8)
- Improved surrogate data for nonlinearity tests
- Surrogate time series
- Practical implementation of nonlinear time series methods: The TISEAN package
- Generating surrogate data for time series with several simultaneously measured variables
- A kernel method for canonical correlation analysis
- A Robust Method for Detecting Interdependences: Application to Intracranially Recorded EEG
- Learning Driver-Response Relationships from Synchronization Patterns
- Detecting Generalized Synchronization of Chaotic Dynamical Systems: A Kernel-based Method and Choice of Its Parameter