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 2024 | Viewed by 3785

Special Issue Editors


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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

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

Published Papers (2 papers)

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Research

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 2 | Viewed by 1144
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 2 | Viewed by 1213
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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