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Relation between HVG-irreversibility and persistence in the modified Langevin equation
Luciano Telesca1, Zbigniew Czechowski2
1National Research Council, Institute of Methodologies for Environmental Analysis, C.da S. Loja, 85050 Tito (PZ), Italy.
Chaos (Woodbury, N.Y.)
|August 3, 2018
Summary
This study reveals that time-irreversibility in modified Langevin equations increases with persistence or antipersistence. This finding, using Kullback-Leibler Divergence (KLD), has implications for understanding population dynamics and ecosystem health.
Area of Science:
- Statistical Physics
- Complex Systems Analysis
- Dynamical Systems Theory
Background:
- Persistence and antipersistence are key properties of time series data.
- Time-irreversibility quantifies the directionality of a system's evolution.
- The Horizontal Visibility Graph (HVG) offers a method to analyze time series properties.
Purpose of the Study:
- To investigate the relationship between persistence/antipersistence and time-irreversibility.
- To apply Kullback-Leibler Divergence (KLD) within the directed HVG framework.
- To analyze a modified Langevin equation with a persistence parameter 'd'.
Main Methods:
- Utilized the directed Horizontal Visibility Graph (HVG) method.
- Employed Kullback-Leibler Divergence (KLD) to quantify irreversibility.
- Analyzed a modified Langevin equation incorporating a persistence parameter 'd'.
Main Results:
- A non-trivial relationship between KLD and the persistence parameter 'd' was identified (KLD(d)).
- The relationship KLD(d) exhibited a non-symmetric shape.
- Results indicate that time-irreversibility intensifies with increasing persistence or antipersistence.
Conclusions:
- Time-irreversibility is intrinsically linked to the persistence properties of the system.
- The non-symmetric KLD(d) relationship provides a novel quantitative measure.
- Findings are applicable to population growth models, offering insights into stability and ecosystem health.
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