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Recent Advances in Complex Dynamics in Non-Smooth Systems
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Recent Advances in Complex Dynamics in Non-Smooth Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 2140

Special Issue Editors

Prof. Dr. Zhouchao Wei

E-Mail Website
Guest Editor
School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan 430074, China
Interests: bifurcation and chaos
Special Issues, Collections and Topics in MDPI journals
Dr. Liguo Yuan

E-Mail Website
Guest Editor
Department of Mathematics, College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642, China
Interests: chaos and bifurcation; fractional-order differential equation; optimization algorithm; image encryption
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Chaos is a common phenomenon in nature and exists in various nonlinear systems. The theoretical research on chaos has lasted for decades. Various definitions and properties of chaos, the theoretical basis and framework of chaos, the correlation between chaos and fractal, and the test methods of chaos have made great progress. At the same time, chaos has also been widely used, such as chaotic image encryption, chaotic secure communication, chaotic optimization algorithms, etc. With the development of nonlinear dynamics, chaotic phenomena have been found in recent nonlinear systems, such as fractional differential systems, fractional discrete systems, discontinuous dynamical systems, etc. In the last 30 years, non-smooth dynamics, including chaos, bifurcation and other mechanisms, have also been found in these new systems. Nonlinear systems, bifurcation, chaos and fractals are intertwined, which constitute several major topics in the study of nonlinear dynamics. Therefore, we organized this Special Issue to collect the latest progress in the research of non-smooth dynamics, such as nonlinear dynamics, chaos, fractal and other nonlinear phenomena.

This Special Issue will showcase articles (e.g., reviews, original papers and comments) on topics including, but not limited to, the following:

  • Nonlinear dynamics in systems such as biological systems, mechanical systems, etc., mainly including new theories, new discoveries and new applications such as chaos, bifurcation and fractals;
  • The latest discovery of chaos and various bifurcation phenomena in nonlinear systems;
  • The latest development of chaos test methods;
  • Attractors and hidden attractors in nonlinear systems;
  • Measurement of fractal sets in nonlinear systems;
  • The latest application research progress of chaos and fractals;
  • Research on various bifurcations of non-smooth systems.

Prof. Dr. Zhouchao Wei
Dr. Liguo Yuan
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • chaos
  • bifurcation
  • attractor
  • non-smooth dynamics

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

22 pages, 1001 KiB  
Article
Complex Dynamics and PID Control Strategies for a Fractional Three-Population Model
by Yan Zhou, Zhuang Cui and Ruimei Li
Mathematics 2024, 12(23), 3793; https://doi.org/10.3390/math12233793 - 30 Nov 2024
Viewed by 637
Abstract
In recent decades, there have been many studies on Hopf bifurcation and population stability with time delay. However, the stability and Hopf bifurcation of fractional-order population systems with time delay are lower. In this paper, we discuss the dynamic behavior of a fractional-order [...] Read more.
In recent decades, there have been many studies on Hopf bifurcation and population stability with time delay. However, the stability and Hopf bifurcation of fractional-order population systems with time delay are lower. In this paper, we discuss the dynamic behavior of a fractional-order three-population model with pregnancy delay using Laplace transform of fractional differential equations, stability and bifurcation theory, and MATLAB software. The specific conditions of local asymptotic stability and Hopf bifurcation for fractional-order time-delay systems are determined. A fractional-order proportional–integral–derivative (PID) controller is applied to the three-population food chain system for the first time. The convergent speed and vibration amplitude of the system can be changed by PID control. For example, after fixing the values of the integral control gain ki and the differential control gain kd, the amplitude of the system decreases and the convergence speed changes as the proportional control gain kp decreases. The effectiveness of the PID control strategy in complex ecosystem is proved. The numerical simulation results are in good agreement with the theoretical analysis. The research in this paper has potential application values concerning the management of complex population systems. The bifurcation theory of fractional-order time-delay systems is also enriched. Full article
(This article belongs to the Special Issue Recent Advances in Complex Dynamics in Non-Smooth Systems)
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11 pages, 252 KiB  
Article
The Global Existence and Boundedness of Solutions to a Chemotaxis–Haptotaxis Model with Nonlinear Diffusion and Signal Production
by Beibei Ai and Zhe Jia
Mathematics 2024, 12(16), 2577; https://doi.org/10.3390/math12162577 - 21 Aug 2024
Cited by 2 | Viewed by 753
Abstract
In this paper, we investigate the following chemotaxis–haptotaxis system (1) with nonlinear diffusion and signal production under homogenous Neumann boundary conditions in a bounded domain with smooth boundary. Under suitable conditions on the data we prove the following: (i) For [...] Read more.
In this paper, we investigate the following chemotaxis–haptotaxis system (1) with nonlinear diffusion and signal production under homogenous Neumann boundary conditions in a bounded domain with smooth boundary. Under suitable conditions on the data we prove the following: (i) For 0<γ≤2n, if α>γ−k+1 and β>1−k, problem (1) admits a classical solution (u,v,w) which is globally bounded. (ii) For 2n<γ≤1, if α>γ−k+1e+1 and β>max{(nγ−2)(nγ+2k−2)2n−k+1,(nγ−2)(γ+1e)n−k+1} or α>γ−k+1 and β>max{(nγ−2)(nγ+2k−2)2n−k+1,(nγ−2)(α+k−1)n−k+1}, problem (1) admits a classical solution (u,v,w) which is globally bounded. Full article
(This article belongs to the Special Issue Recent Advances in Complex Dynamics in Non-Smooth Systems)
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