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Fractal Fract
Special Issues
Analysis and Modeling of Fractional-Order Dynamical Networks
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Analysis and Modeling of Fractional-Order Dynamical Networks

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

Deadline for manuscript submissions: closed (31 October 2024) | Viewed by 2444

Special Issue Editors

Dr. Wang Fei

E-Mail Website
Guest Editor
School of Mathematical Science, Qufu Normal University, Qufu 273165, China
Interests: synchronization control of dynamic network systems; fractional-order systems; fractional-order neural networks
Dr. Feifei Du

E-Mail Website
Guest Editor
College of Science, Northwest A&F University, Xianyang 712100, China
Interests: fractional-order neural networks; fractional-order complex networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, fractional-order systems have received extensive attention, and the study of dynamic network systems coupled by nodes with fractional-order dynamics has attracted more and more scholars. Certain kinds of fractional-order dynamical networks have been investigated and achieved many outstanding results, such as fractional-order neural networks, fractional-order gene regulatory networks, fractional-order multi-agent systems, etc. Stability, synchronization and consensus are hot topics for these fractional-order networks. This Special Issue focuses on the modeling, dynamic characteristics, and control theory of fractional-order dynamic network systems, as well as their application in practical engineering.

In this Special Issue, we invite review and original research papers dealing with recent developments in the analysis and modeling of fractional-order dynamical networks, as well as practical developments in various science and engineering fields, including mathematics and physics.

This Special Issue will focus on, but not be limited to, the following:

(1) Fractional-order neural networks;

(2) Fractional-order gene regulatory networks;

(3) Fractional-order dynamical networks;

(4) Fractional-order multi-agent systems;

(5) Coupled fractional-order systems;

(6) Synchronization control of fractional-order systems;

(6) Mathematical modeling of fractional complex systems;

(7) Heterogeneous networks.

Dr. Wang Fei
Dr. Feifei Du
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 systems
  • neural networks
  • gene regulatory networks
  • dynamical networks
  • multi-agent systems
  • coupled systems
  • synchronization control
  • heterogeneous networks
  • analysis of dynamic behavior

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Published Papers (3 papers)

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18 pages, 559 KiB  
Article
Finite-Time Synchronization Criteria for Caputo Fractional-Order Uncertain Memristive Neural Networks with Fuzzy Operators and Transmission Delay Under Communication Feedback
by Hongguang Fan, Kaibo Shi, Zizhao Guo and Anran Zhou
Fractal Fract. 2024, 8(11), 619; https://doi.org/10.3390/fractalfract8110619 - 23 Oct 2024
Viewed by 621
Abstract
Unlike existing memristive neural networks or fuzzy neural networks, this article investigates a class of Caputo fractional-order uncertain memristive neural networks (CFUMNNs) with fuzzy operators and transmission delay to realistically model complex environments. Especially, the fuzzy symbol AND and the fuzzy symbol OR [...] Read more.
Unlike existing memristive neural networks or fuzzy neural networks, this article investigates a class of Caputo fractional-order uncertain memristive neural networks (CFUMNNs) with fuzzy operators and transmission delay to realistically model complex environments. Especially, the fuzzy symbol AND and the fuzzy symbol OR as well as nonlinear activation behaviors are all concerned in the generalized master-slave networks. Based on the characteristics of the neural networks being studied, we have designed distinctive information feedback control protocols including three different functional sub-modules. Combining comparative theorems, inequality techniques, and stability theory, novel delay-independent conditions can be derived to ensure the finite-time synchronization (FTS) of fuzzy CFUMNNs. Besides, the upper bound of the settling time can be effectively evaluated based on feedback coefficients and control parameters, which makes the achievements of this study more practical for engineering applications such as signal encryption and secure communications. Ultimately, simulation experiments show the feasibility of the derived results. Full article
(This article belongs to the Special Issue Analysis and Modeling of Fractional-Order Dynamical Networks)
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17 pages, 3103 KiB  
Article
Distributed Consensus Tracking of Incommensurate Heterogeneous Fractional-Order Multi-Agent Systems Based on Vector Lyapunov Function Method
by Conggui Huang and Fei Wang
Fractal Fract. 2024, 8(10), 575; https://doi.org/10.3390/fractalfract8100575 - 30 Sep 2024
Viewed by 561
Abstract
This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate [...] Read more.
This paper investigates the tracking problem of fractional-order multi-agent systems. Both the order and parameters of the leader are unknown. Firstly, based on the positive system approach, the asymptotically stable criteria for incommensurate linear fractional-order systems are derived. Secondly, the models of incommensurate heterogeneous multi-agent systems are introduced. To cope with incommensurate and heterogeneous situations among followers and the leader, radial basis function neural networks (RBFNNs) and a discontinuous control method are used. Thirdly, the consensus criteria are derived by using the Vector Lyapunov Function method. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical method. Full article
(This article belongs to the Special Issue Analysis and Modeling of Fractional-Order Dynamical Networks)
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21 pages, 473 KiB  
Article
Mittag-Leffler Synchronization in Finite Time for Uncertain Fractional-Order Multi-Delayed Memristive Neural Networks with Time-Varying Perturbations via Information Feedback
by Hongguang Fan, Xijie Chen, Kaibo Shi, Yaohua Liang, Yang Wang and Hui Wen
Fractal Fract. 2024, 8(7), 422; https://doi.org/10.3390/fractalfract8070422 - 19 Jul 2024
Cited by 4 | Viewed by 873
Abstract
To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function [...] Read more.
To construct a nonlinear fractional-order neural network reflecting the complex environment of the real world, this paper considers the common factors such as uncertainties, perturbations, and delays that affect the stability of the network system. In particular, not only does the activation function include multiple time delays, but the memristive connection weights also consider transmission delays. Stemming from the characteristics of neural networks, two different types of discontinuous controllers with state information and sign functions are devised to effectuate network synchronization objectives. Combining the finite-time convergence criterion and the theory of fractional-order calculus, Mittag-Leffler synchronization conditions for fractional-order multi-delayed memristive neural networks (FMMNNs) are derived, and the upper bound of the setting time can be confirmed. Unlike previous jobs, this article focuses on applying different inequality techniques in the synchronous analysis process, rather than comparison principles to manage the multi-delay effects. In addition, this study removes the restrictive requirement that the activation function has a zero value at the switching jumps, and the discontinuous control protocol in this paper makes the networks achieve synchronization over a finite time, with some advantages in terms of the convergence speed. Full article
(This article belongs to the Special Issue Analysis and Modeling of Fractional-Order Dynamical Networks)
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