2010
DOI: 10.1007/s00422-009-0362-1
|View full text |Cite
|
Sign up to set email alerts
|

The identification of critical fluctuations and phase transitions in short term and coarse-grained time series—a method for the real-time monitoring of human change processes

Abstract: We introduce two complementary measures for the identification of critical instabilities and fluctuations in natural time series: the degree of fluctuations F and the distribution parameter D. Both are valid measures even of short and coarse-grained data sets, as demonstrated by artificial data from the logistic map (Feigenbaum-Scenario). A comparison is made with the application of the positive Lyapunov exponent to time series and another recently developed complexity measure-the Permutation Entropy. The resu… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

1
111
0
7

Year Published

2013
2013
2020
2020

Publication Types

Select...
6
2
1

Relationship

2
7

Authors

Journals

citations
Cited by 120 publications
(124 citation statements)
references
References 27 publications
(20 reference statements)
1
111
0
7
Order By: Relevance
“…Importantly, as a dynamical system approaches a phase transition, the constraints among the system's components begin to break down. A number of methods have been proposed as a means of detecting these phase transitions, such as changes in variability and autocorrelation (Dakos, Van Nes, D'Odorico, & Scheffer, 2012), examining shifts in the values to which the system is attracted (Butler, 2011), changes in entropy and power law scaling (Stephen, Boncoddo, Magnuson, & Dixon, 2009;Stephen, Dixon, & Isenhower, 2009), measures of fluctuation (Schiepek & Strunk, 2010), and, more qualitatively, cognitive event analysis (Steffensen, Vall ee-Tourangeau, & Vall ee-Tourangeau, 2016).…”
Section: Dynamical Systems and Phase Transitionsmentioning
confidence: 99%
“…Importantly, as a dynamical system approaches a phase transition, the constraints among the system's components begin to break down. A number of methods have been proposed as a means of detecting these phase transitions, such as changes in variability and autocorrelation (Dakos, Van Nes, D'Odorico, & Scheffer, 2012), examining shifts in the values to which the system is attracted (Butler, 2011), changes in entropy and power law scaling (Stephen, Boncoddo, Magnuson, & Dixon, 2009;Stephen, Dixon, & Isenhower, 2009), measures of fluctuation (Schiepek & Strunk, 2010), and, more qualitatively, cognitive event analysis (Steffensen, Vall ee-Tourangeau, & Vall ee-Tourangeau, 2016).…”
Section: Dynamical Systems and Phase Transitionsmentioning
confidence: 99%
“…Concerning technology for high-frequency process monitoring, an important contribution has been made with the introduction of the "Synergetic Navigation System" by Schiepek & Strunk (2010). This software package is able to send out daily questionnaires that have been developed specifically for process monitoring, like the therapy process questionnaire (TPB, Schiepek, Aichhorn, & Strunk, 2012), but also outcome-related measures and other instruments.…”
Section: Introductionmentioning
confidence: 99%
“…For situations where timeseries measurement is principally possible, but not at the order of several hundred data points, other complexity properties than fractal scaling can be investigated, which are indicative of IDD and suitable for shorter timeseries (e.g., Schiepek and Strunk 2010;Webber and Zbilut 1994), but whose relationship to fractal scaling has yet to be clarified.…”
Section: Interaction-dominant Dynamicsmentioning
confidence: 99%