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Universality classes of fluctuation dynamics in hierarchical complex systems.
A M S Macêdo1, Iván R Roa González1, D S P Salazar2
1Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco 50670-901 Recife, Pernambuco, Brazil.
Physical Review. E
|April 19, 2017
Summary
This study introduces a unified statistical approach for complex systems, revealing two distinct dynamics classes that explain signal tails in turbulence and finance.
Area of Science:
- Complex Systems Science
- Statistical Physics
- Time Series Analysis
Background:
- Multiscale complex systems exhibit intricate short-time dynamics.
- Understanding the statistical behavior of these systems is crucial for various scientific fields.
Purpose of the Study:
- To propose a unified statistical approach for describing the short-time dynamics of multiscale complex systems.
- To identify the underlying mechanisms governing the statistical properties of complex system signals.
Main Methods:
- Representing the probability density function (PDF) of time series as a statistical superposition.
- Formulating background dynamics using a hierarchical stochastic model derived from physical constraints.
- Utilizing Meijer G functions for representing signal and background probability distributions.
Main Results:
- The proposed model successfully describes the statistics of short-time dynamics in complex systems.
- Two universality classes for background dynamics were identified, leading to power-law and stretched-exponential signal tails.
- Empirical data from classical turbulence and financial markets showed excellent agreement with the theoretical predictions.
Conclusions:
- The unified approach provides a robust framework for analyzing complex system dynamics.
- The identified universality classes offer insights into the fundamental behavior of diverse complex systems.
- The theory's validation with empirical data underscores its broad applicability.