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Decomposing Spectral and Phasic Differences in Nonlinear Features between Datasets
Pedro A M Mediano1, Fernando E Rosas2,3,4, Adam B Barrett5
1Department of Psychology, University of Cambridge, Cambridge CB2 3EB, United Kingdom.
This study introduces a novel method to distinguish true nonlinear phenomena from spectral and phasic effects in complex systems. The approach decomposes observed differences, enhancing time series analysis.
Area of Science:
- Complex Systems Analysis
- Nonlinear Dynamics
- Time Series Analysis
Background:
- Characterizing complex systems often involves nonlinear methods.
- Distinguishing genuine nonlinear phenomena from spectral and phasic influences is a key challenge.
- Simpler spectral methods may not capture all complex system dynamics.
Purpose of the Study:
- To quantify the impact of spectral and phasic effects on nonlinear features.
- To develop a method for decomposing observed differences in nonlinear features between systems or states.
- To provide a more nuanced understanding of nonlinear phenomena.
Main Methods:
- Derivation of a decomposition from a sequence of null models.
- Quantification of spectral, phasic, and spectrum-phase interaction components.
- Approach makes no assumptions about data structure.
Main Results:
- A method to decompose the difference in an observable into distinct components.
- Separation of spectral, phasic, and their interaction effects.
- Identification of genuine nonlinear phenomena.
Conclusions:
- The derived decomposition adds nuance to nonlinear time series analysis.
- The method is applicable across various data structures.
- Enables more accurate characterization of complex systems.
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