Complexity, Fractals, and Nonlinear Phenomena Across Disciplines

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 371

Special Issue Editors


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Guest Editor
1. Faculty of Engineering, Uninettuno University, 00186 Rome, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione Roma Tor Vergata, 00133 Rome, Italy
3. Istituto di Astrofisica e Planetologia Spaziali–INAF, 00133 Rome, Italy
Interests: fractal analysis; particle physics; astrophysics; geophysics; space science

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Guest Editor
Department of Applied Mathematics, Kaunas University of Technology, 51368 Kaunas, Lithuania
Interests: fractal analysis; theoretical neuroscience; neural signal processing; statistical analysis; deep learning; complex systems

Special Issue Information

Dear Colleagues,

This Special Issue focuses on the methodological frameworks for  investigating fractal and complex systems. Studies may span mathematics, physics, environmental science, biomedical signals, neuroscience, social systems, and other domains characterized by nonlinear and fractal dynamics.

We welcome contributions addressing the stability, interpretability, and fractal properties of nonlinear measures in complex systems through theoretical and data-driven modelling. This Issue encourages the development, evaluation, and application of robust fractal measures that explicitly account for measurement uncertainties. Fractal analysis provides powerful tools to capture multiscale complexity, self-similarity, and irregular patterns, enhancing the understanding of nonlinear dynamics across diverse scales. Topics of interest include the following:

  • Fractal indicators of nonlinearity in natural and living systems;
  • Sensitivity of measures to data processing and resolution;
  • Comparative assessment of feature extraction methods;
  • Predictive performance and statistical validation of nonlinear measures.

Dr. Livio Conti
Dr. Karolina Armonaite
Guest Editors

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 2700 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 analysis
  • non-linear measures
  • statistical analysis
  • uncertainty estimates
  • information theory
  • complex systems
  • neuroscience
  • astrophysics
  • particle physics

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Published Papers (1 paper)

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Research

33 pages, 13986 KB  
Article
Chaotic Heat Flows and Kolmogorov Entropy in a Basin Geomorphology: A First Approximation Study of Their Effects on the Fractal Dimension
by Patricio Pacheco, Eduardo Mera, Denisse Cartagena-Ramos, Javier Wachter and Constanza Salinas
Fractal Fract. 2026, 10(4), 240; https://doi.org/10.3390/fractalfract10040240 - 3 Apr 2026
Viewed by 219
Abstract
This study investigates, at a microscale, urban sensible heat flux and Kolmogorov entropy in locations with varying degrees of urban densification according to regular geometries, and examines their effect on fractal dimension. To this end, an ultrasonic anemometer was installed in each of [...] Read more.
This study investigates, at a microscale, urban sensible heat flux and Kolmogorov entropy in locations with varying degrees of urban densification according to regular geometries, and examines their effect on fractal dimension. To this end, an ultrasonic anemometer was installed in each of four locations spread across a 648 km2 area within a basin geomorphology. This anemometer measures the horizontal and vertical components of wind speed and sonic temperature. The measurements for each variable constitute hourly time series of 3968 data points. From the time series of vertical wind speed and sonic temperature, the hourly sensible heat flux was calculated using the statistical technique of covariances. The total heat calculated for each location during the measurement period indicates which location contributes the greatest heat flux to the boundary layer. Applying chaos theory to the hourly sensible heat time series shows that all series are chaotic, and the Kolmogorov entropy can be obtained for each. The chaotic analysis of data from different locations reveals a proportional relationship between heat flux emissions, Kolmogorov entropy, and urban densification, amplifying the Kolmogorov cascade effect. The vertical components of the wind studied result from the interaction of the wind with the geometric regularity of the buildings, which causes increases in both heat flow and Kolmogorov entropy, suggesting a relationship of these quantities with the decay of the fractal dimension. Full article
(This article belongs to the Special Issue Complexity, Fractals, and Nonlinear Phenomena Across Disciplines)
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