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Multiscale characterization of recurrence-based phase space networks constructed from time series
Ruoxi Xiang1, Jie Zhang, Xiao-Ke Xu
1Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong, People's Republic of China. rxxiang@gmail.com
Chaos (Woodbury, N.Y.)
|April 3, 2012
Summary
This study explores complex networks derived from time series data. We found network properties reveal insights into dynamical systems, distinguishing periodic from chaotic behaviors.
Area of Science:
- Complex systems analysis
- Time series analysis
- Network science
Background:
- Complex network theory offers tools to analyze time series data.
- Network topological properties can reveal distinct information about dynamical systems.
Purpose of the Study:
- To systematically investigate the recurrence-based phase space network of order k.
- To analyze network properties for characterizing different dynamical systems.
Main Methods:
- Construction of recurrence-based phase space networks of order k.
- Analysis of global network properties (size, degree distribution).
- Analysis of local network properties (vertex degree, clustering coefficients, betweenness centrality).
Main Results:
- Network size scales with different scale exponents.
- Degree distribution exhibits a quasi-symmetric bell shape around 2k.
- Local network properties correlate with local orbit stability.
Conclusions:
- Recurrence-based phase space networks provide valuable insights into time series dynamics.
- Network topology effectively distinguishes between periodic and chaotic systems.
- Local network properties offer complementary information regarding system stability.
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