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Fractal Fract
Special Issues
Design, Optimization and Applications for Fractional Chaotic System
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Design, Optimization and Applications for Fractional Chaotic System

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

Deadline for manuscript submissions: 15 December 2025 | Viewed by 7551

Special Issue Editors

Prof. Dr. José Cruz Nunez-Perez

E-Mail Website
Guest Editor
Instituto Politécnico Nacional, IPN-CITEDI, Ave. Instituto Politécnico Nacional 1310, Tijuana 22430, BC, Mexico
Interests: analog and digital circuits design; circuit modelling; chaotic oscillators design; EA optimization; RF circuits; FPGA realization
Dr. Vincent Ademola Adeyemi

E-Mail Website
Guest Editor
Instituto Politécnico Nacional, IPN-CITEDI, Ave. Instituto Politécnico Nacional 1310, Tijuana 22430, BC, Mexico
Interests: chaotic nonlinear dynamical systems; secure communication systems; cryptosystems; system optimization; FPGA system design; image processing

Special Issue Information

Dear Colleagues,

Fractional calculus is a mathematical subject that has been widely applied in engineering and physics for centuries. Many systems in aerodynamics, mechatronics, electrical circuits, biology, fluid flows, chemistry, electromagnetic waves, dielectric polarization, and many more are modeled as fractional order systems. Because of groundbreaking research by pioneering scientists in nonlinear dynamical system, in the last few decades, the subject of chaos has attracted great interest from researchers. In this manner, fractional order chaotic systems have been investigated in recent times. Therefore, investigations have led to the development of many chaotic systems, and there are several activities in areas such as electronic realization, stability, synchronization, optimization, and chaos-based communication.

The field of fractional-order chaotic circuits and systems refers to a class of electronics that incorporate concepts from fractional calculus into their chaotic behavioral modeling and design. Using these concepts to design analog and digital circuits is the focus of research on their integration into electronic circuits, filters, chaotic oscillators, memory devices, and control systems. The fractional order offered with these design approaches provides additional flexibility and tuning for target specifications. Additionally, the use of evolutionary algorithms for optimizing fractional order chaotic systems, biological materials, energy storage devices, secure communication systems, and circuit elements with fractional-order impedances are being widely explored.

The focus of this Special Issue is to continue to advance research on topics relating to the theory, design, implementation, optimization, and application of fractional and integer order chaotic circuits and systems. Topics that are invited for submission include (but are not limited to):

  • Applications of fractional-order chaotic systems for telecommunication systems;
  • Applications of fractional-order chaotic circuits for biology and biomedicine;
  • Applications of fractional-order chaotic models for memory elements;
  • Active and passive designs of fractional-order electromagnetic elements;
  • Digital and analog approximations for realization of fractional-order chaotic systems;
  • FPGA realization of chaos circuits and systems;
  • Fractional-order chaos theory;
  • Fractional-order chaotic filter and oscillator designs and realizations;
  • Fractional-order chaos systems, control and their implementation;
  • Fractional-order chaos mem-elements, modeling and applications;
  • Hyperchaotic fractional-order system;
  • Optimization of fractional-order chaotic systems;
  • Synchronization of fractional-order chaotic systems.

Prof. Dr. José Cruz Nunez-Perez
Dr. Vincent Ademola Adeyemi
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • applications of chaotic systems and circuits
  • chaos
  • fractional-order circuits
  • fractional-order systems
  • fractional-order models
  • fractional-order mem-elements
  • hyperchaos
  • optimization
  • synchronization

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Published Papers (4 papers)

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Research

21 pages, 2014 KiB  
Article
A New Chaotic Weak Signal Detection Method Based on a Simplified Fractional-Order Genesio–Tesi Chaotic System
by Hongcun Mao, Yuling Feng, Xiaoqian Wang, Chao Gao, Changhao Lin and Zhihai Yao
Fractal Fract. 2025, 9(2), 74; https://doi.org/10.3390/fractalfract9020074 - 24 Jan 2025
Viewed by 368
Abstract
The detection of weak signals is a well-established application in chaos theory. This theory leverages the inherent robustness of chaotic systems, enabling them to resist noise and thus serve as effective tools for identifying weak signals. However, challenges remain in selecting appropriate chaotic [...] Read more.
The detection of weak signals is a well-established application in chaos theory. This theory leverages the inherent robustness of chaotic systems, enabling them to resist noise and thus serve as effective tools for identifying weak signals. However, challenges remain in selecting appropriate chaotic systems and in their practical implementation—areas that are still under-explored. In this paper, we analyze a simplified fractional-order Genesio–Tesi chaotic system, which exhibits a unique chaos-divergence characteristic. Based on this characteristic, we propose a new detection method that uses the chaos-divergence state as a criterion for determining the presence or absence of a signal when detecting weak signal amplitudes. This approach makes the simplified fractional-order Genesio–Tesi chaotic system more suitable for chaotic weak signal detection. Notably, the significant variance observed in the divergent state’s independent variables emerges as a key feature, enhancing the system’s ability to detect the frequencies of weak signals. Our numerical simulations focus on detecting weak cosine signals masked by three different types of noise. The results demonstrate successful detection of a weak signal at a frequency of 100 rad/s under the specified conditions, with the lowest detectable signal-to-noise ratio of −40.83 dB. Overall, these results highlight the effectiveness and feasibility of our proposed method for weak signal detection. Full article
(This article belongs to the Special Issue Design, Optimization and Applications for Fractional Chaotic System)
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24 pages, 527 KiB  
Article
Analyzing the Chaotic Dynamics of a Fractional-Order Dadras–Momeni System Using Relaxed Contractions
by Haroon Ahmad, Fahim Ud Din, Mudasir Younis and Liliana Guran
Fractal Fract. 2024, 8(12), 699; https://doi.org/10.3390/fractalfract8120699 - 27 Nov 2024
Viewed by 690
Abstract
This paper is inspired by cutting-edge advancements in chaos theory, fractional calculus, and fixed point theory, which together provide a powerful framework for examining the dynamics of complex systems. At the heart of our research is the fractional-order Dadras–Momeni chaotic system, a pivotal [...] Read more.
This paper is inspired by cutting-edge advancements in chaos theory, fractional calculus, and fixed point theory, which together provide a powerful framework for examining the dynamics of complex systems. At the heart of our research is the fractional-order Dadras–Momeni chaotic system, a pivotal model in chaos theory celebrated for its intricate, multi-scroll dynamics. Leveraging the Atangana–Baleanu fractional derivative, we extend fractional computation to chaotic systems, offering deeper insights into their behavior. To fortify the mathematical foundation of our analysis, we employ the relaxed θ rational contractions in the realm of metric spaces, enabling a more precise exploration of the system’s dynamics. A key goal of this work is to simplify the definition of the function class Θ while maintaining the existence and uniqueness of fixed points under θ-relaxed contractions, integrating this framework with the established literature on complete metric spaces. We explore the system’s behavior across six distinct cases by varying δ with a fixed fractional order of ℏ=0.98. In the first case, a single scroll forms, while successive cases lead to increased scrolls—reaching up to four by the sixth case. Phase portraits and time series analyses reveal a progression in complexity and chaos, with denser, intertwined scrolls as δ increases. This behavior highlights the system’s heightened sensitivity to parameter variations, demonstrating how fractional parameters influence the chaotic dynamics. Our results offer meaningful contributions to both the theoretical foundations and practical applications of chaos theory and fractional calculus, advancing the understanding of chaotic systems in new and impacted ways. Full article
(This article belongs to the Special Issue Design, Optimization and Applications for Fractional Chaotic System)
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23 pages, 2062 KiB  
Article
Fractional PID Controller for Voltage-Lift Converters
by Luis M. Martinez-Patiño, Francisco J. Perez-Pinal, Allan Giovanni Soriano-Sánchez, Manuel Rico-Secades, Carina Zarate-Orduño and Jose-Cruz Nuñez-Perez
Fractal Fract. 2023, 7(7), 542; https://doi.org/10.3390/fractalfract7070542 - 13 Jul 2023
Cited by 4 | Viewed by 1739
Abstract
Voltage-lift is a widely used technique in DC–DC converters to step-up output voltage levels. Several traditional and advanced control techniques applicable to power electronic converters (PEC) have been reported and utilized for voltage-lift applications. Similarly, in recent years the implementation of fractional-order controllers [...] Read more.
Voltage-lift is a widely used technique in DC–DC converters to step-up output voltage levels. Several traditional and advanced control techniques applicable to power electronic converters (PEC) have been reported and utilized for voltage-lift applications. Similarly, in recent years the implementation of fractional-order controllers (FOC) in PEC applications has gained interest, aiming to improve system performance, and has been validated in basic converter topologies. Following this trend, this work presents an FOC for a voltage-lift converter, requiring only output voltage feedback. A third-order non-minimal phase system is selected for experimentation to verify FOC implementations for more complex PEC configurations. A simple, straightforward design and approximation methodology for the FOC is proposed. Step-by-step development of the FOC, numerical and practical results on a 50 W voltage-lift converter are reported. The results show that PEC transient and steady-state responses can be enhanced using FOC controllers when compared with classical linear controllers. Extended applications of FOC for improved performance in power conversion is also discussed. Full article
(This article belongs to the Special Issue Design, Optimization and Applications for Fractional Chaotic System)
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31 pages, 6927 KiB  
Article
FPGA Implementation of Parameter-Switching Scheme to Stabilize Chaos in Fractional Spherical Systems and Usage in Secure Image Transmission
by Vincent-Ademola Adeyemi, Esteban Tlelo-Cuautle, Yuma Sandoval-Ibarra and Jose-Cruz Nuñez-Perez
Fractal Fract. 2023, 7(6), 440; https://doi.org/10.3390/fractalfract7060440 - 30 May 2023
Cited by 4 | Viewed by 2430
Abstract
The main objective of this work was to implement the parameter-switching chaos control scheme for fractional-order spherical systems and develop a chaos-based image encryption and transmission system. The novelty in the developed secure communication system is the application of the parameter-switching scheme in [...] Read more.
The main objective of this work was to implement the parameter-switching chaos control scheme for fractional-order spherical systems and develop a chaos-based image encryption and transmission system. The novelty in the developed secure communication system is the application of the parameter-switching scheme in the decryption of RGB and grayscale images, which undergo one round of encryption using the chaotic states of the fractional system and a diffusion process. The secure communication system has a synchronized master and slave topology, resulting in transmitter and receiver systems for encrypting and decrypting images, respectively. This work was demonstrated numerically and also implemented on two FPGAs, namely Artix-7 AC701 and Cyclone V. The results show that the parameter-switching scheme controls chaos in the fractional-order spherical systems effectively. Furthermore, the performance analysis of the image encryption and transmission system shows that there is no similarity between the original and encrypted images, while the decryption of the encrypted images is without a loss of quality. The best result in terms of the encryption was obtained from the chaotic state x of the fractional-order system, with correlation coefficients of 0.0511 and 0.0392 for the RGB and grayscale images, respectively. Finally, the utilization of the FPGA logical resources shows that the implementation on Artix-7 AC701 is more logic-efficient than on Cyclone V. Full article
(This article belongs to the Special Issue Design, Optimization and Applications for Fractional Chaotic System)
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