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Mathematics
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Nonlinear Dynamics, Chaos, and Mathematical Physics
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Nonlinear Dynamics, Chaos, and Mathematical Physics

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 2763

Special Issue Editor

Prof. Dr. Masoud Asadi-Zeydabadi

E-Mail Website
Guest Editor
Department of Physics, University of Colorado Denver, 1201 Larimer St., Denver, CO 80204, USA
Interests: nonlinear dynamics and chaos; biological modeling and medical physics

Special Issue Information

Dear Colleagues, 

The applications of nonlinear dynamics and chaos theory span a wide range of disciplines, offering valuable insights into complex systems and phenomena. In physics, chaotic behavior is observed in systems such as turbulent fluid flow and celestial mechanics. In engineering, the study of chaos aids in designing robust and efficient systems, particularly in fields like control theory and signal processing. Biological systems, such as neural networks, exhibit nonlinear dynamics, and chaos theory helps unravel the intricate patterns underlying these phenomena. Additionally, economics and finance use chaos theory, as it provides a framework for understanding the unpredictable nature of markets and economic systems. Disease dynamics, weather forecasting, ecological dynamics, and even social systems can be analyzed through the lens of nonlinear dynamics, highlighting the versatility and applicability of this theoretical framework across diverse scientific and practical domains.

Topics include, but are not limited to, the following:

  • Control Systems and Robotics;
  • Hamiltonian Chaos;
  • Fluid Dynamics and Turbulence;
  • Weather Forecasting and Climate Modeling;
  • Neural Networks and Brain Dynamics;
  • Communication Systems and Signal Processing;
  • Coupled Nonlinear Oscillators and Synchronization;
  • Epidemiology and Disease Dynamics;
  • Ecological Systems and Population Dynamics;
  • Financial Markets and Economic Systems;
  • Nonlinear Data  Analysis;
  • Topology and Chaos.

Prof. Dr. Masoud Asadi-Zeydabadi
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. 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

  • control systems
  • robotics
  • chaos
  • dynamics
  • signal processing
  • data analysis
  • topology

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

Published Papers (3 papers)

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Research

23 pages, 498 KB  
Article
On the Existence and Uniqueness of Two-Dimensional Nonlinear Fuzzy Difference Equations with Logarithmic Interactions
by Yasser Almoteri and Ahmed Ghezal
Mathematics 2025, 13(21), 3532; https://doi.org/10.3390/math13213532 - 4 Nov 2025
Viewed by 23
Abstract
This paper investigates a new class of two-dimensional fuzzy difference equations that integrate logarithmic nonlinearities with interaction effects between system variables. Motivated by the need to model complex dynamical systems influenced by uncertainty and interdependencies, we propose a system that extends existing one-dimensional [...] Read more.
This paper investigates a new class of two-dimensional fuzzy difference equations that integrate logarithmic nonlinearities with interaction effects between system variables. Motivated by the need to model complex dynamical systems influenced by uncertainty and interdependencies, we propose a system that extends existing one-dimensional models to capture more realistic interactions within a discrete-time framework. Our approach employs the characterization theory to transform the fuzzy system into an equivalent family of classical difference equations, thereby facilitating a rigorous analysis of the existence, uniqueness, and boundedness of positive solutions. To support the theoretical findings, two numerical examples are provided, illustrating the model’s capacity to capture complex dynamical patterns under fuzzy conditions. An application to a fuzzy population growth model illustrates how the model captures both interaction effects and uncertainty while ensuring well-defined and stable solutions. Numerical simulations show that, for instance, with α=0.10, β=δ=1.0, γ=0.08, and ρx=ρy=0.10, the trajectories of (xt,yt) rapidly converge toward a stable fuzzy equilibrium, with uncertainty bands confirming the positivity and boundedness of the solutions. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos, and Mathematical Physics)
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17 pages, 283 KB  
Article
Closed-Form Solutions of a Nonlinear Rational Second-Order Three-Dimensional System of Difference Equations
by Messaoud Berkal, Taha Radwan, Mehmet Gümüş, Raafat Abo-Zeid and Karim K. Ahmed
Mathematics 2025, 13(20), 3327; https://doi.org/10.3390/math13203327 - 18 Oct 2025
Viewed by 220
Abstract
In this paper, we investigate the behavior of solutions to a nonlinear system of rational difference equations of order two, defined by [...] Read more.
In this paper, we investigate the behavior of solutions to a nonlinear system of rational difference equations of order two, defined by xn+1=xnyn−1yn(a+bxnyn−1),yn+1=ynzn−1zn(c+dynzn−1),zn+1=znxn−1xn(e+fznxn−1), where n denotes a nonzero integer; the parameters a,b,c,d,e,f are real constants; and the initial conditions x−1,x0,y−1,y0,z−1,z0 are nonzero real numbers. By applying a suitable variable transformation, we reduce the original coupled system to three independent rational difference equations. This allows for separate analysis using established methods for second-order nonlinear recurrence relations. We derive explicit solutions and examine the qualitative behavior, including boundedness and periodicity, under different conditions. Our findings contribute to the theory of rational difference equations and offer insights for higher-order systems in applied sciences. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos, and Mathematical Physics)
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20 pages, 312 KB  
Article
Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations
by Hashem Althagafi and Ahmed Ghezal
Mathematics 2024, 12(8), 1159; https://doi.org/10.3390/math12081159 - 12 Apr 2024
Cited by 3 | Viewed by 1635
Abstract
This paper aims to derive analytical expressions for solutions of fractional bidimensional systems of difference equations with higher-order terms under specific parametric conditions. Additionally, formulations of solutions for one-dimensional equations derived from these systems are explored. Furthermore, rigorous proof is provided for the [...] Read more.
This paper aims to derive analytical expressions for solutions of fractional bidimensional systems of difference equations with higher-order terms under specific parametric conditions. Additionally, formulations of solutions for one-dimensional equations derived from these systems are explored. Furthermore, rigorous proof is provided for the local stability of the unique positive equilibrium point of the proposed systems. The theoretical findings are validated through numerical examples using MATLAB, facilitating graphical illustrations of the results. Full article
(This article belongs to the Special Issue Nonlinear Dynamics, Chaos, and Mathematical Physics)
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