Complexity Descriptors from Different Disciplines: Links and Applications

Topic Information

Dear Colleagues,

The study of non-linear dynamical systems or the analysis of time series through chaos theory, geometric theory (fractals, multifractals), information theory (entropies), complexity theory (Kolmogorov complexity, Lempel-ziv complexity, ...), ..., have allowed the development of new descriptors capable of better classifying, predicting the functioning/behavior of systems or time series.

The fact of having approached this problem from several angles has also allowed highlighting bridges between these different theories and an increased understanding of the complex systems studied; however, some links remain hidden or even unexploited.

On the other hand, the list of descriptors that can be used to characterize, qualify, and quantify a system/time series/biological sequence is becoming increasingly long, and for neophytes, the choice of certain descriptors can sometimes be difficult. Seeking to highlight bridges and similarities between these different existing descriptors could facilitate greater enlightenment for informing the selection of certain descriptors and even assisting in improving understanding of the problem under consideration.

To initiate the reflection, several existing examples (non-exhaustive list) showing bridges between disciplines are presented below in addition to some suggested avenues for further exploration:

• The concept of self-organized criticality has allowed a better understanding of “stable” states at several scales, leading to the development of multi-scale descriptors/invariants such as fractals and multi-fractals, and a link between the theory of chaotic dynamical systems and fractal geometry has been highlighted;
• The concept of a recurrence graph, which results from the projection of a multidimensional phase space onto a two-dimensional space, has allowed better describing the dynamics of a system, especially when moving from one type of transition to another. The set of descriptors quantifying recurrences (RQA) is based on the search for similar patterns and a number of these descriptors, such as the sample entropy, which allows a bridge with information theory and recurrences from phase diagrams. The correlation integral, fractal dimension of attractors, and Lyapunov exponents are other well-known examples.
• The analysis of fundamental properties such as the symmetry of patterns (e.g., palindromes), either directly from time series or from recurrence graphs, can lead to the development of descriptors sensitive to symmetry variations, such as the irreversibility factor, symmetry or symmentropy, to name but a few. A bridge between information theory, geometric theory, and dynamical systems theory is thus created.

This Special Issue provides an opportunity to highlight links that are still hidden or unexploited or even create new ones. There is also an opportunity to take stock of these different links in order to help the researcher choose the most appropriate descriptors for his or her problem.

Prof. Dr. Jean-Marc Girault
Prof. Dr. Tuan D. Pham
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Entropy entropy	2.7	4.7	1999	20.8 Days	CHF 2600
Fractal and Fractional fractalfract	5.4	3.6	2017	18.9 Days	CHF 2700
Dynamics dynamics	-	-	2021	12.7 Days	CHF 1000
Symmetry symmetry	2.7	4.9	2009	16.2 Days	CHF 2400

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Published Papers (1 paper)