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Fractal Fract
Special Issues
Fractional Diffusion, Multistability and Control in Complex Systems
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Fractional Diffusion, Multistability and Control in Complex Systems

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

Deadline for manuscript submissions: 31 October 2024 | Viewed by 3097

Special Issue Editor

Prof. Dr. Mingshu Peng

E-Mail Website
Guest Editor
School of Science, Beijing Jiaotong University, No 3. Shangyuancun, Haidian District, Beijing 100044, China
Interests: differential equations; bifurcation and chaos of nonlinear dynamical system; complex networks; numerical methods

Special Issue Information

Dear Colleagues,

There is a significant amount of research exploring reaction–diffusion models related to biological pattern formation. The practical use of reaction–diffusion models has increased remarkably in recent decades. The mechanochemical theory of biological pattern and form has played an important role in furthering our understanding of biology. Models and their biological predictions have become a stimulant for guiding critical experiments that can result in significant discoveries. This, naturally, should be the aim of any mathematical biology modeling. Spatial patterns are very complex in nature, and can play a significant role on the stability, as well as spatio-temporal behavior, of the population dynamical system because of the interactions between the species and the natural environment. For instance, it was reported that the shape of the ecological communities could be greatly affected by the spatial structure of species interaction. The main reason may lie in the diversely distributed resources in nature between populations in different habitats.

This Special Issue aims to focus on fractional diffusion, multistability and control in complex systems. Related topics, such as general mathematics analysis, Turing instability, bifurcation theory, complexity, control theory, mathematical modelling, numerical and computational methods, etc., will be considered for publication.

Prof. Dr. Mingshu Peng
Guest Editor

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

  • turing instability
  • multistability
  • bifurcation
  • chaos
  • fractal differential equations
  • complexity
  • mathematical modelling
  • control
  • critical point theory
  • boundary value problem
  • stability
  • delay
  • diffusion
  • pattern formation
  • spatio-temporal behavior
  • related practical problem

Published Papers (3 papers)

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Research

25 pages, 59053 KiB  
Article
Comparisons for Global Dynamics of a Geometrically Nonlinear Oscillator among Single-, Double- and Quadruple-Well Configurations
by Huihang Sun and Huilin Shang
Fractal Fract. 2024, 8(4), 202; https://doi.org/10.3390/fractalfract8040202 - 29 Mar 2024
Viewed by 688
Abstract
This paper conducts a comparative analysis of the global dynamics of a harmonically excited oscillator with geometrical nonlinearities. Static analysis of the oscillatory system shows that adjusting the horizontal distance ratio from 1 to 0 can lead to single, double and quadruple well [...] Read more.
This paper conducts a comparative analysis of the global dynamics of a harmonically excited oscillator with geometrical nonlinearities. Static analysis of the oscillatory system shows that adjusting the horizontal distance ratio from 1 to 0 can lead to single, double and quadruple well configurations successively. Intra-well and inter-well resonant responses are deduced analytically. Qualitative and quantitative results both reveal that the oscillator displays the stiffness–softening characteristic in cases of double and quadruple wells and the stiffness–hardening characteristic in the case of a single well. The initial-sensitive phenomenon jump is performed via fractal basins of attraction. Complex dynamical behaviors, including higher-order periodic responses and chaos, are also exhibited. The results demonstrate that the oscillator with a double or quadruple well configuration can achieve the inter-well response with large displacement, thus confirming its desirability in engineering applications of geometrically nonlinear oscillators. Full article
(This article belongs to the Special Issue Fractional Diffusion, Multistability and Control in Complex Systems)
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20 pages, 1498 KiB  
Article
Adaptive Fault-Tolerant Control for Consensus of Nonlinear Fractional-Order Multi-Agent Systems with Diffusion
by Yuqian Yang, Qingwen Qi, Jingyao Hu, Jiashu Dai and Chengdong Yang
Fractal Fract. 2023, 7(10), 760; https://doi.org/10.3390/fractalfract7100760 - 16 Oct 2023
Cited by 1 | Viewed by 971
Abstract
This paper mainly studies fault-tolerant control for a class of semi-linear fractional-order multi-agent systems with diffusion characteristics, where the actuator fault is considered. The adaptive fault-tolerant control protocol based on the adjacency relationship of agents is firstly designed, which can adjust the coupling [...] Read more.
This paper mainly studies fault-tolerant control for a class of semi-linear fractional-order multi-agent systems with diffusion characteristics, where the actuator fault is considered. The adaptive fault-tolerant control protocol based on the adjacency relationship of agents is firstly designed, which can adjust the coupling gain online through the adaptive mechanism. Using the Lyapunov stability theory, the adaptive fault-tolerant control protocol can drive the agents to achieve consensus for leader-following and leaderless cases. Finally, the simulation experiment is carried out, showing the effectiveness of the proposed theory. Full article
(This article belongs to the Special Issue Fractional Diffusion, Multistability and Control in Complex Systems)
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24 pages, 652 KiB  
Article
Unraveling the Dynamics of Singular Stochastic Solitons in Stochastic Fractional Kuramoto–Sivashinsky Equation
by M. Mossa Al-Sawalha, Humaira Yasmin, Rasool Shah, Abdul Hamid Ganie and Khaled Moaddy
Fractal Fract. 2023, 7(10), 753; https://doi.org/10.3390/fractalfract7100753 - 12 Oct 2023
Cited by 8 | Viewed by 1075
Abstract
This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the modified extended direct algebraic method (mEDAM). Comprehensive contour, 3D, and 2D visual representations [...] Read more.
This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the modified extended direct algebraic method (mEDAM). Comprehensive contour, 3D, and 2D visual representations clearly depict the categorization of these stochastic soliton solutions as kink waves or shock waves, offering a clear description of these soliton behaviors within the context of the SFKSE framework. The paper also illustrates the flexibility of the transformation-based approach mEDAM for investigating soliton occurrence not only in SFKSE but also in a wide range of nonlinear fractional partial differential equations (FPDEs). Furthermore, the analysis considers the effect of noise, specifically Brownian motion, on soliton solutions and wave dynamics, revealing the significant influence of randomness on the propagation, generation, and stability of soliton in complex stochastic systems and advancing our understanding of extreme behaviors in scientific and engineering domains. Full article
(This article belongs to the Special Issue Fractional Diffusion, Multistability and Control in Complex Systems)
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