Nonlinear Dynamics, Chaos, and Mathematical Physics

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

Deadline for manuscript submissions: 31 July 2024 | Viewed by 614

Special Issue Editor


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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

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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

Published Papers (1 paper)

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Research

20 pages, 312 KiB  
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
Viewed by 438
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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