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Modeling, Fractal, and Multifractional Artificial Intelligence of Complex Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (30 January 2024) | Viewed by 2106

Special Issue Editor


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Guest Editor
Department of Mathematics, “Al. I. Cuza” University of Iasi, 700506 Iasi, Romania
Interests: set-valued measures; non-additive measures; set-valued integrals; non-additive integrals; topology; fractals; multifractals; nonlinear dynamics
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Special Issue Information

Dear Colleagues,

For this issue, we propose the use of fractal–multifractal theories in describing the dynamics of complex systems. By complex system, we mean the set of entities in nonlinear interaction at various scales of resolution, from the microscopic to the macroscopic scale. In such a context, dynamics at the subatomic, atomic, molecular, mesoscopic, intragalactic, and extragalactic scale will be considered. Dynamics analyses can also be extended to biological systems. All these dynamic descriptions must be based on notions and concepts such as entropy in the Shannon, Fischer, fractal sense, etc., as well as on the role of invariants that can be built based on the concepts of entropy and informational energy (multifractal entropy, informational energy in the sense of Onicescu, etc.)

Dr. Alina Cristiana Gavriluţ
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal
  • multifractal
  • scale relativity
  • entropy
  • informational energy
  • scale resolution
  • harmonic mappings

Published Papers (2 papers)

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14 pages, 2964 KiB  
Article
Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics
by Vlad Ghizdovat, Oana Rusu, Mihail Frasila, Cristina Marcela Rusu, Maricel Agop and Decebal Vasincu
Entropy 2023, 25(8), 1149; https://doi.org/10.3390/e25081149 - 31 Jul 2023
Viewed by 914
Abstract
Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, [...] Read more.
Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. In this way, a non-differentiable description of complex systems dynamics can become functional, even in the case of standard theories (General Relativity and Quantum Mechanics). Full article
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17 pages, 1304 KiB  
Article
Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion
by Decebal Vasincu, Andreea Bianca Bruma, Oana Rusu, Cristina Marcela Rusu, Vlad Ghizdovat and Maricel Agop
Entropy 2023, 25(8), 1143; https://doi.org/10.3390/e25081143 - 30 Jul 2023
Viewed by 616
Abstract
Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of [...] Read more.
Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates. Full article
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