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Fractal Fract
Special Issues
Fractional-Order Chaotic Systems and Circuits: Design, Modeling and Implementation
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Fractional-Order Chaotic Systems and Circuits: Design, Modeling and Implementation

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

Deadline for manuscript submissions: closed (20 February 2024) | Viewed by 7937

Special Issue Editors

Dr. Akif Akgül

E-Mail Website
Guest Editor
Department of Computer Engineering, Faculty of Engineering, Hitit University, Corum 19030, Turkey
Interests: nonlinear dynamics; chaos; chaotic systems; nonlinear circuits; fractals
Prof. Dr. Esteban Tlelo-Cuautle

E-Mail Website
Guest Editor
Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Tonantinztla, Puebla 72840, Mexico
Interests: analog signal processing; integrated circuits; optimization by meta-heuristics; fractional-order chaotic systems; security in internet of things; analog/RF and mixed-signal design automation tools
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Studies on fractional-order systems have increased significantly in recent years. Fractional-order systems can enable one to understand the existence characteristics of complex natural, physical, chemical, medical, scientific and engineering-related systems in more depth. It is also important to note that the potential to implement theoretical fractional-order chaotic systems plays a critical role in real-world applications. Accordingly, this Special Issue focuses on the circuit application of fractional-order chaotic systems for exploring the recent advances in modeling, design, theory, dynamic analysis and implementation. The Special Issue, thus, aims to publish the possible scientific advances in the field of the fractional-order systems addressing both the practical and theoretical aspects. To this end, original research as well as review articles are welcome for our Special Issue.

Potential topics include, but are not limited to, the following:

  • Fractional calculus;
  • Modeling and analysis of fractional-order circuits;
  • Modeling electronic and electrical devices;
  • Fractional-order chaotic circuits and systems;
  • Fractional-order circuit theory;
  • Fractional-order filter and oscillator designs and realizations;
  • Digital and analog approximations for realization of fractional-order systems;
  • Active and passive designs of fractional-order elements;
  • The fractional-order circuit models for real-world applications.

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 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

  • chaos
  • chaotic systems
  • fractional-order systems
  • circuit design
  • electronic circuit implementations

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Published Papers (4 papers)

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Research

26 pages, 7699 KiB  
Article
Extreme Homogeneous and Heterogeneous Multistability in a Novel 5D Memristor-Based Chaotic System with Hidden Attractors
by Chengwei Dong and Min Yang
Fractal Fract. 2024, 8(5), 266; https://doi.org/10.3390/fractalfract8050266 - 28 Apr 2024
Cited by 2 | Viewed by 1250
Abstract
This paper proposes a novel five-dimensional (5D) memristor-based chaotic system by introducing a flux-controlled memristor into a 3D chaotic system with two stable equilibrium points, and increases the dimensionality utilizing the state feedback control method. The newly proposed memristor-based chaotic system has line [...] Read more.
This paper proposes a novel five-dimensional (5D) memristor-based chaotic system by introducing a flux-controlled memristor into a 3D chaotic system with two stable equilibrium points, and increases the dimensionality utilizing the state feedback control method. The newly proposed memristor-based chaotic system has line equilibrium points, so the corresponding attractor belongs to a hidden attractor. By using typical nonlinear analysis tools, the complicated dynamical behaviors of the new system are explored, which reveals many interesting phenomena, including extreme homogeneous and heterogeneous multistabilities, hidden transient state and state transition behavior, and offset-boosting control. Meanwhile, the unstable periodic orbits embedded in the hidden chaotic attractor were calculated by the variational method, and the corresponding pruning rules were summarized. Furthermore, the analog and DSP circuit implementation illustrates the flexibility of the proposed memristic system. Finally, the active synchronization of the memristor-based chaotic system was investigated, demonstrating the important engineering application values of the new system. Full article
(This article belongs to the Special Issue Fractional-Order Chaotic Systems and Circuits: Design, Modeling and Implementation)
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24 pages, 15749 KiB  
Article
MO-CCCII-Based Single-Input Multi-Output (SIMO) Current-Mode Fractional-Order Universal and Shelving Filter
by Fadile Sen, Ali Kircay, Buket Sonbas Cobb and Akif Akgul
Fractal Fract. 2024, 8(4), 181; https://doi.org/10.3390/fractalfract8040181 - 22 Mar 2024
Cited by 1 | Viewed by 1190
Abstract
This study introduces an innovative filter topology capable of providing simultaneous positive and negative gain outputs for one-fractional order LP, with high-pass, all-pass, and fractional-order shelving filter responses. The circuit, utilizing multi-output second-generation current-controlled conveyors, stands out as the first to deliver ten [...] Read more.
This study introduces an innovative filter topology capable of providing simultaneous positive and negative gain outputs for one-fractional order LP, with high-pass, all-pass, and fractional-order shelving filter responses. The circuit, utilizing multi-output second-generation current-controlled conveyors, stands out as the first to deliver ten outputs, incorporating both integer and fractional-order filter responses, without requiring additional components. Its current-mode design simplifies the process, employing minimal active and grounded passive elements, making it appropriate for low-voltage/low-power applications. The filter utilizes fifth-order Oustaloup approximation and Foster type-I RC networks for fractional-order capacitors, providing enhanced control over the transition slope. PSpice simulations confirmed a 1 kHz cut-off, showcasing low power consumption, minimal noise, and a wide dynamic range, positioning the filter as suitable for sensors, control, and acoustic applications. Full article
(This article belongs to the Special Issue Fractional-Order Chaotic Systems and Circuits: Design, Modeling and Implementation)
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15 pages, 3717 KiB  
Article
Real-Time Synchronisation of Multiple Fractional-Order Chaotic Systems: An Application Study in Secure Communication
by Bachir Nail, Mahedi Abdelghani Atoussi, Slami Saadi, Imad Eddine Tibermacine and Christian Napoli
Fractal Fract. 2024, 8(2), 104; https://doi.org/10.3390/fractalfract8020104 - 8 Feb 2024
Cited by 6 | Viewed by 2203
Abstract
In this paper, we use two Fractional-Order Chaotic Systems (FOCS)—one for the sender and one for the receiver—to determine the optimal synchronisation for a secure communication technique. With the help of the Step-By-Step Sliding-Mode Observer (SBS-SMO), this synchronisation is accomplished. An innovative optimisation [...] Read more.
In this paper, we use two Fractional-Order Chaotic Systems (FOCS)—one for the sender and one for the receiver—to determine the optimal synchronisation for a secure communication technique. With the help of the Step-By-Step Sliding-Mode Observer (SBS-SMO), this synchronisation is accomplished. An innovative optimisation method, known as the artificial Harris hawks optimisation (HHO), was employed to enhance the observer’s performance. This method eliminates the random parameter selection process and instead selects the optimal values for the observer. In a short amount of time, the secret message that could have been in the receiver portion (signal, voice, etc.) was successfully recovered using the proposed scheme. The experimental validation of the numerical results was carried out with the assistance of an Arduino microcontroller and several electronic components. In addition, the findings of the experiments were compared with the theoretical calculations, revealing a satisfactory level of agreement. Full article
(This article belongs to the Special Issue Fractional-Order Chaotic Systems and Circuits: Design, Modeling and Implementation)
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17 pages, 10832 KiB  
Article
Circuit Realization of the Fractional-Order Sprott K Chaotic System with Standard Components
by Abdullah Gokyildirim
Fractal Fract. 2023, 7(6), 470; https://doi.org/10.3390/fractalfract7060470 - 13 Jun 2023
Cited by 11 | Viewed by 1917
Abstract
Interest in studies on fractional calculus and its applications has greatly increased in recent years. Fractional-order analysis has the potential to enhance the dynamic structure of chaotic systems. This study presents the implementation of a lower-order fractional electronic circuit using standard components for [...] Read more.
Interest in studies on fractional calculus and its applications has greatly increased in recent years. Fractional-order analysis has the potential to enhance the dynamic structure of chaotic systems. This study presents the implementation of a lower-order fractional electronic circuit using standard components for the Sprott K system. To our knowledge, there are no chaotic circuit realizations in the literature where the value of a fractional-order parameter is approximately 0.8, making this study pioneering in this aspect. Additionally, various numerical analyses of the system are conducted, including chaotic time series and phase planes, Lyapunov exponents, spectral entropy (SE), and bifurcation diagrams, in order to examine its dynamic characteristics and complexity. As anticipated, the voltage outputs obtained from the oscilloscope demonstrated good agreement with both the numerical analysis and PSpice simulations. Full article
(This article belongs to the Special Issue Fractional-Order Chaotic Systems and Circuits: Design, Modeling and Implementation)
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