Journal ArticleDOI
Alternating Locking Ratios in Imperfect Phase Synchronization
TLDR
In this article, it was shown that the phase drift is caused by the passage near the long unstable periodic orbits whose frequencies are locked by external force in ratios different from 1:1.Abstract:
In periodically driven chaotic dynamical systems with a broad distribution of intrinsic time scales, perfect phase synchronization cannot be reached. Long segments of evolution during which the phase of a chaotic variable follows the phase of the driving force are interrupted by short segments of phase drift. We demonstrate that this drift is another short-lived synchronized state; its onset is caused by the passage near the long unstable periodic orbits whose frequencies are locked by external force in ratios different from 1:1.read more
Citations
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Journal ArticleDOI
Complex networks: Structure and dynamics
TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
Journal ArticleDOI
The synchronization of chaotic systems
TL;DR: Synchronization of chaos refers to a process where two chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy) as discussed by the authors.
Journal ArticleDOI
Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients
TL;DR: In this paper, the authors apply the concept of phase synchronization of chaotic and/or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms (EEGs) recorded from patients with temporal lobe epilepsy.
Journal ArticleDOI
Reply to ``Comment on `Performance of different synchronization measures in real data: A case study on electroencephalographic signals' ''
TL;DR: It is claimed that the applied measures used in the synchronization between left and right hemisphere rat electroencephalographic channels are valuable for the study of synchronization in real data and in the particular case of EEG signals their use as complementary variables could be of clinical relevance.
Journal ArticleDOI
Performance of different synchronization measures in real data: A case study on electroencephalographic signals
TL;DR: In this article, the synchronization between left and right hemisphere rat electroencephalographic (EEG) channels by using various synchronization measures, namely nonlinear interdependences, phase synchronizations, mutual information, cross correlation, and the coherence function, was studied.
References
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Book
The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors
TL;DR: The first homoclinic explosion in the Lorenz equation was described in this article, where the authors proposed an approach to the problem of finding the position of the first homocalinic explosion by using the Maxima-in-z method.