Detecting direction of coupling in interacting oscillators.
@article{Rosenblum2001DetectingDO, title={Detecting direction of coupling in interacting oscillators.}, author={Michael Rosenblum and Arkady Pikovsky}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2001}, volume={64 4 Pt 2}, pages={ 045202 } }
We propose a method for experimental detection of directionality of weak coupling between two self-sustained oscillators from bivariate data. The technique is applicable to both noisy and chaotic systems that can be nonidentical or even structurally different. We introduce an index that quantifies the asymmetry in coupling.
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References
SHOWING 1-10 OF 33 REFERENCES
Phase Synchronization in Regular and Chaotic Systems
- PhysicsInt. J. Bifurc. Chaos
- 2000
This contribution presents a brief introduction to the theory of synchronization of selfsustained oscillators, and the basic notions of phase and frequency locking are reconsidered within a common framework.
Measuring statistical dependence and coupling of subsystems
- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000
It is demonstrated that it is indeed possible to obtain nontrivial directional information, but it is also argued that the interpretation of this information is difficult.
Phase synchronization of chaotic oscillators.
- PhysicsPhysical review letters
- 1996
The new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators is presented, and a relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.
Measuring information transfer
- Computer SciencePhysical review letters
- 2000
An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time and is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble.
- BiologyPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1996
Dynamical interdependence, perhaps generalized synchrony, was identified in this neuronal network between simultaneous single unit firings, between units and the population, and betweenunits and intracellular EPSP’s.
Learning driver-response relationships from synchronization patterns.
- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000
We test recent claims that causal (driver-response) relationships can be deduced from interdependencies between simultaneously measured time series. We apply two recently proposed interdependence…
A robust method for detecting interdependences: application to intracranially recorded EEG
- Computer Science
- 1999
Asymptotically stable phase synchronization revealed by autoregressive circle maps
- MathematicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000
A specially designed of nonlinear time series analysis based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates, allows us to detect conditional asymptotic stability of coupled phases.