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New Advances in Nonlinear Dynamics Theory and Applications
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New Advances in Nonlinear Dynamics Theory and Applications

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

Deadline for manuscript submissions: 31 January 2026 | Viewed by 662

Special Issue Editors

Dr. Fei Yu

E-Mail Website
Guest Editor
School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China
Interests: chaotic systems; chaotic circuits; memristor; neural networks; complex network; chaos-based applications
Special Issues, Collections and Topics in MDPI journals
Dr. Jingru Sun

E-Mail Website
Guest Editor
College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Interests: memristive neuromorphic circuit; neuromorphic computation; firing pattern; neurodynamics
Dr. Jun Mou

E-Mail Website
Guest Editor
School of Information Science and Engineering, Dalian polytechnic University, Dalian 116034, China
Interests: chaos; chaotic circuits; memristor neural networks; fractional-order system; information security
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since Huygens witnessed two types of nonlinear phenomena in 1673, namely the significant deviation of a pendulum from isochronism and the synchronization of dual frequency clocks, the research and development of nonlinear dynamics theory have gone through a difficult period. However, the limitations of research methods at that time resulted in its theoretical system only becoming complete nearly a century ago. It is particularly worth mentioning that in recent decades, the flourishing of bifurcation and chaos research has pushed nonlinear dynamics to the forefront of international disciplines.

The purpose of this Special Issue is to promote the development and application of nonlinear dynamics theory in fields such as mathematics, physics, computer science, information technology, biotechnology, and artificial intelligence. We welcome all innovative research studies on nonlinear dynamics theory and its application development. We look forward to receiving research manuscripts on the topics of chaos, complex systems, memristors, neural networks, synchronous control, system stability, nonlinear circuits, and nonlinear dynamics applications. Please note that the research direction is not limited to the above-mentioned topics.

Dr. Fei Yu
Dr. Jingru Sun
Dr. Jun Mou
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

  • nonlinear dynamics theory and its applications
  • differential equations and difference equations
  • chaotic systems
  • mathematical modeling of complex systems and networks
  • optimization, balance, and stability analysis
  • nonlinear circuits and memristors
  • system synchronization and control

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Published Papers (2 papers)

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14 pages, 3504 KiB  
Article
A Chaotic Butterfly Attractor Model for Economic Stability Assessment in Financial Systems
by Muhamad Deni Johansyah, Sundarapandian Vaidyanathan, Khaled Benkouider, Aceng Sambas, Chittineni Aruna, Sarath Kumar Annavarapu, Endang Rusyaman and Alit Kartiwa
Mathematics 2025, 13(10), 1633; https://doi.org/10.3390/math13101633 - 16 May 2025
Viewed by 31
Abstract
This paper introduces a novel three-dimensional financial risk system that exhibits complex dynamical behaviors, including chaos, multistability, and a butterfly attractor. The proposed system is an extension of the Zhang financial risk model (ZFRM), with modifications that enhance its applicability to real-world economic [...] Read more.
This paper introduces a novel three-dimensional financial risk system that exhibits complex dynamical behaviors, including chaos, multistability, and a butterfly attractor. The proposed system is an extension of the Zhang financial risk model (ZFRM), with modifications that enhance its applicability to real-world economic stability assessments. Through numerical simulations, we confirm the system’s chaotic nature using Lyapunov exponents (LE), with values calculated as L1=3.5547, L2=0, L3=−22.5642, indicating a positive Maximal Lyapunov Exponent (MLE) that confirms chaos. The Kaplan–Yorke Dimension (KYD) is determined as Dk = 2.1575, reflecting the system’s fractal characteristics. Bifurcation analysis (BA) reveals parameter ranges where transitions between periodic, chaotic, and multistable states occur. Additionally, the system demonstrates coexisting attractors, where different initial conditions lead to distinct long-term behaviors, emphasizing its sensitivity to market fluctuations. Offset Boosting Control (OBC) is implemented to manipulate the chaotic attractor, shifting its amplitude without altering the underlying system dynamics. These findings provide deeper insights into financial risk modeling and economic stability, with potential applications in financial forecasting, risk assessment, and secure economic data transmission. Full article
(This article belongs to the Special Issue New Advances in Nonlinear Dynamics Theory and Applications)
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23 pages, 5306 KiB  
Article
Robust Higher-Order Nonsingular Terminal Sliding Mode Control of Unknown Nonlinear Dynamic Systems
by Quanmin Zhu, Jianhua Zhang, Zhen Liu and Shuanghe Yu
Mathematics 2025, 13(10), 1559; https://doi.org/10.3390/math13101559 - 9 May 2025
Viewed by 259
Abstract
In contrast to the majority of model-based terminal sliding mode control (TSMC) approaches that rely on the plant physical model and/or data-driven adaptive pointwise model, this study treats the unknown dynamic plant as a total uncertainty in a black box with enabled control [...] Read more.
In contrast to the majority of model-based terminal sliding mode control (TSMC) approaches that rely on the plant physical model and/or data-driven adaptive pointwise model, this study treats the unknown dynamic plant as a total uncertainty in a black box with enabled control inputs and attainable outputs (either measured or estimated), which accordingly proposes a model-free (MF) nonsingular terminal sliding mode control (MFTSMC) for higher-order dynamic systems to reduce the tedious modelling work and the design complexity associated with the model-based control approaches. The total model-free controllers, derived from the Lyapunov differential inequality, obviously provide conciseness and robustness in analysis/design/tuning and implementation while keeping the essence of the TSMC. Three simulated bench test examples, in which two of them have representatively numerical challenges and the other is a two-link rigid robotic manipulator with two input and two output (TITO) operational mode as a typical multi-degree interconnected nonlinear dynamics tool, are studied to demonstrate the effectiveness of the MFTSMC and employed to show the user-transparent procedure to facilitate the potential applications. The major MFTSMC performance includes (1) finite time (2.5±0.05 s) dynamic stabilization to equilibria in dealing with total physical model uncertainty and disturbance, (2) effective dynamic tracking and small steady state error 0±0.002, (3) robustness (zero sensitivity at state output against the unknown bounded internal uncertainty and external disturbance), (4) no singularity issue in the neighborhood of TSM σ=0, (5) stable chattering with low amplitude (±0.01) at frequency 50 mHz due to high gain used against disturbance d(t)=100+30sin(2πt)). The simulation results are similar to those from well-known nominal model-based approaches. Full article
(This article belongs to the Special Issue New Advances in Nonlinear Dynamics Theory and Applications)
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