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. While both nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems.

References in corpus (37)

• Power-law distributions in empirical data
• Recurrence Plots for the Analysis of Complex Systems
• The structure and dynamics of multilayer networks
• From time series to complex networks: the visibility graph
• Diffusion dynamics on multiplex networks
• Modularity and community detection in bipartite networks
• Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods
• Complex Network Approach for Recurrence Analysis of Time Series
• The backbone of the climate network
• The spatial structure of networks
• Nonlinear time-series analysis revisited
• Long-Time Correlations in the Stochastic Regime
• Estimating Granger causality from Fourier and wavelet transforms of time series data
• Historical Review of Recurrence Plots
• Coupling functions: Universal insights into dynamical interaction mechanisms
• Hydrodynamic provinces and oceanic connectivity from a transport network help designing marine reserves
• The clustering coefficient and community structure of bipartite networks
• Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
• Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods
• Ambiguities in recurrence-based complex network representations of time series
• Bi-clique Communities
• Analytical framework for recurrence-network analysis of time series
• Generalised Recurrence Plot Analysis for Spatial Data
• Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks
• Geometric detection of coupling directions by means of inter-system recurrence networks
• Flow networks: A characterization of geophysical fluid transport
• Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions
• Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods
• Detecting recurrence domains of dynamical systems by symbolic dynamics
• Strategical incoherence regulates cooperation in social dilemmas on multiplex networks
• Quantifying sudden changes in dynamical systems using symbolic networks
• Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions
• Multiplex visibility graphs to investigate recurrent neural networks dynamics
• Overlapping Community Detection in Bipartite Networks
• Clustering coefficient and periodic orbits in flow networks
• Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls
• Geometric and dynamic perspectives on phase-coherent and noncoherent chaos

Cited by in corpus (24)

• Graph-Based Deep Learning for Medical Diagnosis and Analysis: Past, Present and Future
• Trends in recurrence analysis of dynamical systems
• A review on turbulent and vortical flow analyses via complex networks
• Persistence in Complex Systems
• Characterizing stochastic time series with ordinal networks
• Time Series Analysis via Network Science: Concepts and Algorithms
• Visibility graph analysis of economy policy uncertainty indices
• Multifractal characterisation of particulate matter (PM10) time series in the Caribbean basin using visibility graphs
• Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: statistics and visibility graph analysis
• The arrow of time across five centuries of classical music
• Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems
• Revealing recurrent regimes of mid-latitude atmospheric variability using novel machine learning method
• Ordinal methods for a characterization of evolving functional brain networks
• Improving graph-based detection of singular events for photochemical smog agents
• Ordinal Patterns in the Duffing Oscillator: Analyzing Powers of Characterization
• Unveiling the connectivity of complex networks using ordinal transition methods
• Permutation time irreversibility in sleep electroencephalograms: Dependence on sleep stage and the effect of equal values
• Recurrence network analysis in a model tripartite quantum system
• Comparative analysis of time irreversibility and amplitude irreversibility based on joint permutation
• Price graphs: Utilizing the structural information of financial time series for stock prediction
• Random walk with multiple memory channels: a new paradigm
• Horizon Visibility Graphs and Time Series Merge Trees are Dual
• A novel parameter for nonequilibrium analysis in reconstructed state spaces
• A complex network approach to time series analysis with application in diagnosis of neuromuscular disorders