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Fractal Fract
Special Issues
Analysis and Control of Fractional-Order Delay Coupling Networks
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Analysis and Control of Fractional-Order Delay Coupling Networks

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

Deadline for manuscript submissions: closed (15 April 2024) | Viewed by 1676

Special Issue Editors

Dr. Tianwei Zhang

E-Mail Website
Guest Editor
Department of Mathematics, Yunnan University, Kunming 650091, China
Interests: nonlinear dynamics; differential/difference equations; controls
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Jianwen Zhou

E-Mail Website
Guest Editor
Department of Mathematics, Yunnan University, Kunming 650091, China
Interests: nonlinear dynamics; differential/difference equations; controls

Special Issue Information

Dear Colleagues,

Fractional-order coupling networks are networks in which the connections between nodes have a fractional-order property. Traditional network models usually assume that the connections between nodes are based on integer order. However, fractional-order coupling networks consider that the connections between nodes have a fractional order. In terms of applications, fractional-order coupling networks have a wide range of applications. First, they can be used to study the synchronization and stability of networks. Second, fractional-order coupling networks can be used to simulate and predict the behavior of complex systems. In addition, fractional-order coupling networks can be applied to signal processing, image processing and machine learning to provide new ideas and methods for solving problems in these fields. Overall, the fractional-order coupling network is a novel and promising network model with wide application prospects. By studying and applying fractional-order coupling networks, we can better understand and explore the behavior of complex systems and provide new ideas and methods for solving practical problems.

This Special Issue provides an opportunity to showcase recent developments in the analysis and control of fractional-order delay coupling networks.

We encourage you to submit articles on the recent developments in the area of fractional-order delay coupling networks.

Dr. Tianwei Zhang
Prof. Dr. Jianwen Zhou
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

  • differential and difference equations
  • fractional order differential equations
  • impulsive differential equations
  • fractional-order systems
  • distributed-order systems
  • fractional-order neural networks
  • neural network
  • complex network
  • time delay

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Published Papers (1 paper)

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Research

38 pages, 1035 KiB  
Article
Novel Hopf Bifurcation Exploration and Control Strategies in the Fractional-Order FitzHugh–Nagumo Neural Model Incorporating Delay
by Yunzhang Zhang and Changjin Xu
Fractal Fract. 2024, 8(4), 229; https://doi.org/10.3390/fractalfract8040229 - 15 Apr 2024
Viewed by 1286
Abstract
In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order [...] Read more.
In this article, we propose a new fractional-order delay-coupled FitzHugh–Nagumo neural model. Taking advantage of delay as a bifurcation parameter, we explore the stability and bifurcation of the formulated fractional-order delay-coupled FitzHugh–Nagumo neural model. A delay-independent stability and bifurcation conditions for the fractional-order delay-coupled FitzHugh–Nagumo neural model is acquired. By designing a proper PDp controller, we can efficaciously control the stability domain and the time of emergence of the bifurcation phenomenon of the considered fractional delay-coupled FitzHugh–Nagumo neural model. By exploiting a reasonable hybrid controller, we can successfully adjust the stability domain and the bifurcation onset time of the involved fractional delay-coupled FitzHugh–Nagumo neural model. This study shows that when the delay crosses a critical value, a Hopf bifurcation will arise. When we adjust the control parameter, we can find other critical values to enlarge or narrow the stability domain of the fractional-order delay-coupled FitzHugh–Nagumo neural model. In order to check the correctness of the acquired outcomes of this article, we present some simulation outcomes via Matlab 7.0 software. The obtained theoretical fruits in this article have momentous theoretical significance in running and constructing networks. Full article
(This article belongs to the Special Issue Analysis and Control of Fractional-Order Delay Coupling Networks)
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