Geometric signature of complex synchronisation scenarios

@article{Feldhoff2013GeometricSO,
  title={Geometric signature of complex synchronisation scenarios},
  author={J. Feldhoff and R. Donner and J. Donges and N. Marwan and J. Kurths},
  journal={arXiv: Chaotic Dynamics},
  year={2013}
}
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled systems including different types of synchronisation such as phase, lag, generalised, or even complete synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation between two coupled chaotic… Expand
A Novel Measure Inspired by Lyapunov Exponents for the Characterization of Dynamics in State-Transition Networks
TLDR
A network measure for characterizing the dynamics on state-transition networks with special focus on differentiating between chaotic and cyclic modes is introduced, demonstrating a strong sensitivity to boundary crisis suggesting applicability in predicting the collapse of chaos. Expand
Complex network approaches to nonlinear time series analysis
Abstract In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series.Expand
Complex Network Analysis of Recurrences
We present a complex network-based approach to characterizing the geometric properties of chaos by exploiting the pattern of recurrences in phase space. For this purpose, we utilize the basicExpand
Reciprocal characterization from multivariate time series to multilayer complex networks.
TLDR
It is proved that under mild conditions, for the given transformation method, the application of interlayer entropy in networks is equivalent to transfer entropy in time series. Expand
Fractal analysis of recurrence networks constructed from the two-dimensional fractional Brownian motions.
In this study, we focus on the fractal property of recurrence networks constructed from the two-dimensional fractional Brownian motion (2D fBm), i.e., the inter-system recurrence network, the jointExpand
Multiscale complex network for analyzing experimental multivariate time series
TLDR
A reliable method for constructing a multiscale complex network from multivariate time series is proposed and a novel clustering coefficient entropy is developed to assess the derived multiscales complex networks, aiming to characterize the coupled dynamical characteristics underlying multivariateTime series. Expand
Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package.
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling fromExpand
Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor.
TLDR
A possible asymmetric bidirectional coupling between q ˙ ' and p ' is observed to exert a stronger influence on p ' than vice versa, and the directional property of the network measure, namely, cross transitivity is used to analyze the type of coupling existing between the acoustic field and the heat release rate fluctuations. Expand
Recurrence Quantification Analysis
TLDR
Recurrence quantification analysis (RQA) is a method for assessing the complexity, nonlinearity, and nonstationarity of biological time series typically defy quantitative description. Expand
Generalized Synchronization Between ENSO and Hydrological Variables in Colombia: A Recurrence Quantification Approach
We use Recurrence Quantification Analysis (RQA) to study features of Generalized Synchronization (GS) between El Niño-Southern Oscillation (ENSO) and monthly hydrological anomalies (HyAns) ofExpand
...
1
2
3
...

References

SHOWING 1-2 OF 2 REFERENCES
Synchronization - A Universal Concept in Nonlinear Sciences
TLDR
This work discusseschronization of complex dynamics by external forces, which involves synchronization of self-sustained oscillators and their phase, and its applications in oscillatory media and complex systems. Expand
Geometric signature of complex synchronisation scenarios
  • Proc. Natl. Acad. Sci. USA ,
  • 2008