Abstract
We address under what conditions dynamical coupling between chaotic systems can be detected reliably from scalar time series. In particular, we study weakly coupled chaotic systems and focus on the detectability of the correlation dimension of the chaotic invariant set by utilizing the Grassberger-Procaccia algorithm. An algebraic scaling law is obtained, which relates the necessary length of the time series to a key parameter of the system: the coupling strength. The scaling law indicates that an extraordinarily long time series is required for detecting the coupling dynamics.
Original language | English |
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Article number | 036217 |
Pages (from-to) | - |
Number of pages | 5 |
Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |
Volume | 66 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sept 2002 |
Keywords
- STRANGE ATTRACTORS
- GENERALIZED SYNCHRONIZATION
- CORRELATION DIMENSION
- LYAPUNOV EXPONENTS
- CHAOTIC SYSTEMS