Bifurcation, Chaos, and Fractals in Fractional-Order Electrical and Electronic Systems, 2nd Edition

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: 31 August 2026 | Viewed by 1034

Special Issue Editors


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Guest Editor
State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Interests: fractional calculus and its applications in electrical and electronic engineering; bifurcation and chaos in electrical and electronic engineering
Special Issues, Collections and Topics in MDPI journals
School of Physics and Electronics, Central South University, Changsha 410083, China
Interests: fractional calculus and its applications; complex dynamic properties of nonlinear systems; memristor and memristor neural networks; complex networks
Special Issues, Collections and Topics in MDPI journals

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Guest Editor
School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China
Interests: analysis and control of complex nonlinear behaviors in electrical and electronic engineering
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Special Issue Information

Dear Colleagues,

Fractional calculus is the extension and generalization of integer calculus; additionally, compared with integer calculus, fractional calculus has superiority as it is able to more accurately describe models, can more easily improve control performance, and has more freedom in designing controllers. At present, with the rapid development of engineering technology, practical electrical and electronic systems are becoming more and more complex, to the point where most of them should be described by using fractional calculus; thus, the requirements for control performance are also increasing. Meanwhile, a fractional-order controller can guarantee the stable operation of a complex practical electrical and electronic system due to its outstanding advantages. Therefore, the construct of the fractional-order model and the design of the fractional-order controller has become a current hot topic. However, fractional-order electrical and electronic systems have complex dynamical properties; among them, bifurcation, chaos, and fractals are typical nonlinear phenomena and will have an important effect on the system performance. Thus, it is necessary to reveal the underlying mechanism of the occurrence of these typical nonlinear phenomena and design a controller to make these typical nonlinear phenomena disappear.

This Special Issue aims to focus on:

  • Bifurcation, chaos, and fractals in fractional-order electrical and electronic systems and their control;
  • Continuous/discrete modeling and stability analysis of fractional-order electrical and electronic systems;
  • Multi-timescale and entropy analysis of fractional-order electrical and electronic systems;
  • Optimization of the control accuracy for fractional-order electrical and electronic systems;
  • Improvements and applications of fractional calculus in electrical and electronic systems.

Please feel free to read and download all the articles published in our first volume:

https://www.mdpi.com/journal/fractalfract/special_issues/HG83F8H169

Dr. Faqiang Wang
Dr. Shaobo He
Dr. Hongbo Cao
Guest Editors

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Keywords

  • bifurcation and its control chaos and its control
  • fractals and their control
  • fractional-order inductor/capacitor
  • fractional-order memristor/meminductor/memcapacitor
  • fractional-order circuits and systems
  • fractional-order electrical and electronic systems
  • multi-timescale and entropy analysis
  • fractional calculus applications

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Published Papers (1 paper)

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Research

20 pages, 22088 KB  
Article
Chaos and Complexity in a Fractional Discrete Memristor Based on a Computer Virus Model
by Omar Kahouli, Imane Zouak, Sulaiman Almohaimeed, Adel Ouannas, Younès Bahou, Ilyes Abidi and Sarra Elgharbi
Fractal Fract. 2026, 10(4), 229; https://doi.org/10.3390/fractalfract10040229 - 30 Mar 2026
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Abstract
In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends on the state and enhances the propagation dynamics of [...] Read more.
In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends on the state and enhances the propagation dynamics of virus spread. By investigating both matching and non-matching fractional orders, it is then possible to derive useful knowledge with respect to cooperating roles in terms of fractional memory and memristive effects. The complexity behind it is confirmed via 3D phase portraits, bifurcation analysis with LEmax calculation, 0–1 chaos test, and SE complexity. Numerical results reveal rich dynamical phenomena, including periodic oscillations, quasi-periodicity, and strong chaos. In fact, positive LEmax values, Brownian-like trajectories, and high-complexity SE corroborate the chaotic nature of the regimes. Thereby, the fractional-order separation in noncommensurate conditions is a marker of chaotic motion, magnified in the emergently high-dimensional space introduced by the memristive element. As these results indicate that the derivative model proposed here provides an excellent fit for complex viruses present in scaffolds, it may prove to be a useful modeling tool. Full article
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