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Detection of coupling delay: A problem not yet solved
David Coufal1, Jozef Jakubík2, Nikola Jajcay1
1Institute of Computer Science, Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Praha 8, Czech Republic.
Chaos (Woodbury, N.Y.)
|September 3, 2017
Summary
Detecting coupling delays in nonlinear systems using conditional mutual information (CMI) and convergent cross mapping (CCM) is unreliable. Both methods struggle with oscillatory dynamics, indicating the problem is not yet solved.
Area of Science:
- Nonlinear Dynamics
- Complex Systems Analysis
- Time Series Analysis
Background:
- Coupling delay detection is crucial for understanding interactions in dynamical systems.
- Nonparametric methods offer model-free approaches to identify these delays.
Purpose of the Study:
- To evaluate the reliability of two nonparametric methods for detecting coupling delays.
- To compare the performance of the Conditional Mutual Information (CMI) and Convergent Cross Mapping (CCM) methods.
Main Methods:
- Computer simulations of unidirectionally and bidirectionally coupled continuous-time and discrete-time nonlinear dynamical systems.
- Assessment of the Conditional Mutual Information (CMI) method (transfer entropy).
- Assessment of the Convergent Cross Mapping (CCM) method.
Main Results:
- Neither CMI nor CCM methods are generally reliable for coupling delay detection.
- CMI showed higher sensitivity in continuous-time chaotic systems, while CCM was more sensitive in discrete-time systems.
- Both methods produced ambiguous results for systems with strong oscillatory components.
Conclusions:
- Nonparametric detection of coupling delay remains a significant challenge.
- Results from CMI and CCM methods require careful interpretation, especially in oscillatory systems.
- Further research is needed to develop robust methods for coupling delay estimation.
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