Chaotic and Fractal Approaches with AI for Multidisciplinary Modeling and Applications

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Optimization, Big Data, and AI/ML".

Deadline for manuscript submissions: 20 July 2026 | Viewed by 925

Special Issue Editors


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Guest Editor
Department of Computer Engineering, Faculty of Engineering, Hitit University, Corum 19030, Turkey
Interests: nonlinear dynamics; chaos; chaotic systems; nonlinear circuits; fractals
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Special Issue Information

Dear Colleagues,

The rapid integration of chaotic dynamics, fractal structures, and artificial intelligence (AI) has opened new horizons in modeling, prediction, security, optimization, and decision-making across various scientific and engineering domains. Chaotic systems offer rich nonlinear behavior and sensitivity that can enhance AI’s explorative power, while fractal geometry provides scalable patterns and structural insights applicable to high-dimensional and complex datasets.

This Special Issue aims to highlight cutting-edge research that leverages chaotic and fractal methods in combination with AI to address multidisciplinary challenges. We invite high-quality contributions that demonstrate theoretical advancements, algorithmic innovations, or practical applications that bridge nonlinear science with intelligent computational techniques. Submissions are invited on topics including (but not limited to):

  • Fractal-based features and representations in AI models;
  • Chaotic neural networks and chaotic activation functions;
  • Fractal and chaotic approaches for optimization, prediction, and classification;
  • AI-enhanced analysis of chaotic or complex datasets;
  •  Fractional calculus methods integrated with AI algorithms;
  • Fractal geometry in image processing, pattern recognition, and medical diagnostics;
  • Chaotic and fractal modeling for complex physical, biological, or socio-technical systems;
  • Fractal and chaotic methods for time-series forecasting.

We encourage submissions of original research articles, comprehensive reviews, and innovative case studies addressing these topics.

Prof. Dr. Akif Akgül
Prof. Dr. Esteban Tlelo-Cuautle
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

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

  • chaos theory
  • fractals
  • artificial intelligence (AI)
  • neural networks
  • hybrid AI approaches
  • chaotic neural networks
  • fractional calculus
  • engineering applications

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Published Papers (1 paper)

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Research

27 pages, 6375 KB  
Article
Fractal Dimension and Chaotic Dynamics of Multiscale Network Factors in Asset Pricing: A Wavelet Packet Decomposition Approach Based on Fractal Market Hypothesis
by Qiaoqiao Zhu and Yuemeng Li
Fractal Fract. 2026, 10(3), 196; https://doi.org/10.3390/fractalfract10030196 - 16 Mar 2026
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Abstract
The nature of nonlinear dynamics of financial markets results in fractal geometry and chaotic behavior that can be viewed on a variety of scales in time. This paper conducts research on the fractal characteristics of the stock network and its contribution to the [...] Read more.
The nature of nonlinear dynamics of financial markets results in fractal geometry and chaotic behavior that can be viewed on a variety of scales in time. This paper conducts research on the fractal characteristics of the stock network and its contribution to the price of assets based on the Fractal Market Hypothesis (FMH). A multiscale network centrality measure is built based on high-frequency return dependencies to measure the self-similar, scale-invariant nature of inter-stock dependencies. The network factor and portfolio returns are then broken down with the wavelet packet decomposition (WPD) to obtain frequency-domain profiles, which characterize the variability of risk transmission in relation to investment horizons. The profiles are consistent with scaling properties of fractal, but the decomposition does not identify causal pathways on its own. Estimation of fractal dimension by use of the box-counting technique aided by the Hurst exponent analysis reveals that the A-share of China market exhibited long-range dependence and multifractal scaling. Network factor has the largest explanatory power in mid-frequency between the D5 and D6 bands of 32 to 128 days. This intermediary frequency concentration is consistent with the hypothesis of heterogeneous markets, in which the groups of investors with varying time horizons generate scale-related price dynamics. The addition of the network factor to a 6-factor specification lowers the GRS under the 5-factor specification by 31.45 to 17.82 on the same test-asset universe, indicating better cross-sectional coverage in the sample. The estimates of the Lyapunov exponents (0.039) as well as the correlation dimension (D2=4.7) confirm the presence of low-dimensional chaotic processes of the network factor series, but these values are specific to the Chinese A-share market over the 2005–2023 sample period. These results provide a frequency-disaggregated use of network-based factor modeling and suggest that it can be applicable in multiscale portfolio risk management where the investor horizon is not uniform. Full article
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