Journal of Statistical Physics

, Volume 165, Issue 4, pp 681–692 | Cite as

A Method for Identification of Critical States of Open Stochastic Dynamical Systems Based on the Analysis of Acceleration

  • Denis M. FilatovEmail author


A new method of fractal analysis of nonstationary time series for recognition of critical (precatastrophic) and noncritical (quiet) modes of behaviour of open stochastic dynamical systems is developed. The method is a modification of the conventional detrended fluctuation analysis (DFA) technique. Unlike the classical DFA that originates in the R/S analysis and implies investigation of the time series by studying the properties of a mixture of velocities and accelerations, the new method focuses on the study of accelerations only. Because at the most basic level the equations of motion of stochastic dynamical systems are expressions for the acceleration, the suggested method results to be more suitable for recognition of critical and noncritical states. Using both model and real data, we demonstrate superiority of the newly developed method over the conventional DFA and provide a detailed discussion on the topic.


Open stochastic dynamical systems Critical states Precursors of catastrophes Fractal analysis Measure of chaoticity 



The author is grateful to the anonymous referees for their comments that have allowed to clarify and substantially improve the final version of the paper.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Sceptica Scientific Ltd.StockportUK

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