Contrasting chaotic with stochastic dynamics via ordinal transition networks
F Olivares1, M Zanin2, L Zunino3
1Instituto de Física, Pontificia Universidad Católica de Valparaiso (PUCV), 23-40025 Valparaíso, Chile.
Chaos (Woodbury, N.Y.)
|July 3, 2020
Summary
We developed a novel method to distinguish chaotic from stochastic dynamics using network properties. This approach effectively separates linear and non-linear systems, even with noise, proving useful in practical applications.
Area of Science:
- Complex Systems Science
- Nonlinear Dynamics
- Network Science
Background:
- Distinguishing chaotic from stochastic dynamics is crucial in many scientific fields.
- Traditional methods often struggle with noisy or complex systems.
Purpose of the Study:
- To introduce a new representation space for contrasting chaotic and stochastic dynamics.
- To develop a method robust to observational noise.
Main Methods:
- Representing time series as complex networks via ordinal pattern transitions.
- Utilizing permutation entropy (global network quantifier) and minimum node permutation entropy (local network quantifier) to position systems in a 2D plane.
Main Results:
- Chaotic and stochastic systems are successfully distinguished by their unique planar locations.
- The characterization remains robust even when observational noise is present.
- Numerical analysis of chaotic maps and stochastic systems validates the approach.
Conclusions:
- The proposed 2D representation space effectively differentiates linear from non-linear dynamical systems.
- The method is validated through experimental applications, demonstrating practical utility.
- This approach offers a valuable tool for analyzing complex dynamics.
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