Advances in Fractional-Order Chaotic and Complex Systems

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

Deadline for manuscript submissions: 31 January 2025 | Viewed by 986

Special Issue Editors


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Guest Editor
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Interests: fractional-order systems; chaotic circuits; memristor-based chaos; neural networks; neural networks and brain-inspired computing; chaotic image encryption
Special Issues, Collections and Topics in MDPI journals
School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Interests: fractional-order systems; chaotic systems; chaotic circuits; memristor; neural networks; complex network; chaos-based applications
Special Issues, Collections and Topics in MDPI journals
School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Interests: fractional-order systems; nonlinear dynamical systems; complex systems; neural networks and dynamic behavior

Special Issue Information

Dear Colleagues,

Compared with integer-order models, fractional-order models are closer to the real world and have more attractive development prospects which have received increasing attention in recent years. This Special Issue aims to promote the development and application of fractional-order chaos theory in fields such as mathematics, physics, computer science, economics, engineering, and artificial intelligence. Innovative research on the theory and application development of fractional-order chaos is very prevalent. In addition, research papers on discovering new fractional-order chaotic phenomena, constructing new fractional-order chaotic systems, and proposing new applications of fractional-order chaos are also very popular. We look forward to receiving research manuscripts on fractional-order chaotic systems, fractional-order memristors, fractional-order neural networks, fractional-order circuits, fractional-order complex systems, and applications based on fractional-order chaos. In conclusion, potential topics include, but are not limited to, the following:

  • Fractional-order theory;
  • Fractional-order chaotic systems and circuits;
  • Fractional-order memristors;
  • Fractional-order neural networks;
  • Fractional-order complex systems and complex networks;
  • Other Fractional-order non-linear systems and circuits;
  • Applications based on fractional-order chaos.

Prof. Dr. Chunhua Wang
Dr. Fei Yu
Dr. Wei Yao
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

  • fractional-order theory
  • fractional-order systems
  • complex systems
  • chaos
  • chaotic systems
  • chaos applications
  • non-linear systems
  • neural networks

Published Papers (1 paper)

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Research

19 pages, 8637 KiB  
Article
Dynamic Analysis and Field-Programmable Gate Array Implementation of a 5D Fractional-Order Memristive Hyperchaotic System with Multiple Coexisting Attractors
by Fei Yu, Wuxiong Zhang, Xiaoli Xiao, Wei Yao, Shuo Cai, Jin Zhang, Chunhua Wang and Yi Li
Fractal Fract. 2024, 8(5), 271; https://doi.org/10.3390/fractalfract8050271 - 1 May 2024
Cited by 1 | Viewed by 659
Abstract
On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke dimension, and [...] Read more.
On the basis of the chaotic system proposed by Wang et al. in 2023, this paper constructs a 5D fractional-order memristive hyperchaotic system (FOMHS) with multiple coexisting attractors through coupling of magnetic control memristors and dimension expansion. Firstly, the divergence, Kaplan–Yorke dimension, and equilibrium stability of the chaotic model are studied. Subsequently, we explore the construction of the 5D FOMHS, introducing the definitions of the Caputo differential operator and the Riemann–Liouville integral operator and employing the Adomian resolving approach to decompose the linears, the nonlinears, and the constants of the system. The complex dynamic characteristics of the system are analyzed by phase diagrams, Lyapunov exponent spectra, time-domain diagrams, etc. Finally, the hardware circuit of the proposed 5D FOMHS is performed by FPGA, and its randomness is verified using the NIST tool. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Chaotic and Complex Systems)
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