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Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition
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Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition

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

Deadline for manuscript submissions: 30 November 2025 | Viewed by 4508

Special Issue Editors

Prof. Dr. Tongxing Li

grade E-Mail Website
Guest Editor
School of Control Science and Engineering, Shandong University, Jinan 250061, China
Interests: difference and differential equations; partial differential equations; dynamic equation; time scales; control theory; biology applications
Special Issues, Collections and Topics in MDPI journals
Dr. Irena Jadlovská

E-Mail Website
Guest Editor
Department of Mathematics and Theoretical Informatics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia
Interests: qualitative theory; ordinary differential equations; functional differential equations; dynamical systems; mathematical modeling in physical/social/life sciences
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The second volume of our publication continues to delve into the fascinating realm of oscillatory phenomena across the various dynamical systems encountered within the fields of natural sciences and technology. Similarly to the first volume, oscillations remain a ubiquitous feature across diverse disciplines, including physiology, ecosystem dynamics, biochemistry, mechanics, and population dynamics. The prevalence of oscillations underscores the need for a robust theoretical framework, which continues to evolve under the banner of oscillation theory.

This Special Issue is dedicated to the modeling and simulation of nonlinear dynamical systems, where oscillation serves as a fundamental behavior. We invite contributions from researchers who are engaged in oscillation theory or those applying existing tools and methods to investigating oscillatory phenomena within real-world dynamical systems. Of particular interest are studies addressing time-delay systems, where the delay is recognized as a significant contributor to the oscillations in dynamical systems.

We eagerly anticipate submissions furthering our understanding of oscillatory properties and their relationship with various physical processes. Join us in exploring the intricate dynamics of oscillatory systems and their applications across diverse scientific disciplines. We eagerly await your contributions.

Prof. Dr. Tongxing Li
Dr. Irena Jadlovská
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

  • mathematical model
  • oscillation
  • dynamical system
  • delay

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Related Special Issue

Published Papers (5 papers)

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Research

11 pages, 1425 KiB  
Article
Invariant-Based Inverse Engineering for Balanced Displacement of a Cartpole System
by Ion Lizuain, Ander Tobalina and Alvaro Rodriguez-Prieto
Mathematics 2025, 13(8), 1220; https://doi.org/10.3390/math13081220 - 8 Apr 2025
Viewed by 221
Abstract
Adiabaticity is a key concept in physics, but its applications in mechanical and control engineering remain underexplored. Adiabatic invariants ensure robust dynamics under slow changes, but they impose impractical time limitations. Shortcuts to Adiabaticity (STA) overcome these limitations by enabling fast operations with [...] Read more.
Adiabaticity is a key concept in physics, but its applications in mechanical and control engineering remain underexplored. Adiabatic invariants ensure robust dynamics under slow changes, but they impose impractical time limitations. Shortcuts to Adiabaticity (STA) overcome these limitations by enabling fast operations with minimal final excitations. In this work, we set a STA strategy based on dynamical invariants and inverse engineering to design the trajectory of a cartpole, a system characterized by its instability and repulsive potential. The trajectories found guarantee a balanced transport of the cartpole within the small oscillations regime. The results are compared to numerical simulations with the exact non-linear model to set the working domain of the designed protocol. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)
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13 pages, 268 KiB  
Article
Iterative Kneser-Type Criteria for Oscillation of Half-Linear Second-Order Advanced Dynamic Equations
by Taher S. Hassan, Bassant M. El-Matary, Ioan-Lucian Popa, Mouataz Billah Mesmouli, Ismoil Odinaev and Yousef Jawarneh
Mathematics 2025, 13(4), 635; https://doi.org/10.3390/math13040635 - 14 Feb 2025
Viewed by 469
Abstract
This work aims to develop new iterative Kneser-type criteria for determining the oscillatory behaviour of half-linear second-order advanced dynamic equations on arbitrary unbounded-above time scales T. The results extend and refine previously established criteria for these equations while also generalising classical criteria [...] Read more.
This work aims to develop new iterative Kneser-type criteria for determining the oscillatory behaviour of half-linear second-order advanced dynamic equations on arbitrary unbounded-above time scales T. The results extend and refine previously established criteria for these equations while also generalising classical criteria for corresponding ordinary dynamic equations. This study provides a broader and more flexible approach to analysing such systems by introducing iterative methods. Several examples are included to demonstrate the accuracy, usefulness, and adaptability. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)
18 pages, 315 KiB  
Article
Improved Hille-Type and Ohriska-Type Criteria for Half-Linear Third-Order Dynamic Equations
by Taher S. Hassan, Mnaouer Kachout, Bassant M. El-Matary, Loredana Florentina Iambor, Ismoil Odinaev and Akbar Ali
Mathematics 2024, 12(23), 3740; https://doi.org/10.3390/math12233740 - 27 Nov 2024
Viewed by 937
Abstract
In this paper, we examine the oscillatory behavior of solutions to a class of half-linear third-order dynamic equations with deviating arguments [...] Read more.
In this paper, we examine the oscillatory behavior of solutions to a class of half-linear third-order dynamic equations with deviating arguments α2(η)ϕδ2α1ηϕδ1uΔ(η)ΔΔ+p(η)ϕδu(g(η))=0, on an arbitrary unbounded-above time scale T, where η∈[η0,∞)T:=[η0,∞)∩T, η0≥0, η0∈T and ϕζ(w):=wζsgnw, ζ>0. Using the integral mean approach and the known Riccati transform methodology, several improved Hille-type and Ohriska-type oscillation criteria have been derived that do not require some restrictive assumptions in the relevant results. Illustrative examples and conclusions show that these criteria are sharp for all third-order dynamic equations compared to the previous results in the literature. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)
15 pages, 306 KiB  
Article
Some Oscillatory Criteria for Second-Order Emden–Fowler Neutral Delay Differential Equations
by Haifeng Tian and Rongrong Guo
Mathematics 2024, 12(10), 1559; https://doi.org/10.3390/math12101559 - 16 May 2024
Cited by 2 | Viewed by 1171
Abstract
In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case, respectively. Compared with some recent results reported in the literature, we extend [...] Read more.
In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case, respectively. Compared with some recent results reported in the literature, we extend the range of the neutral coefficient. Therefore, our results generalize to some of the results presented in the literature. Furthermore, several examples are provided to illustrate our conclusions. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)
11 pages, 268 KiB  
Article
New Oscillation Criteria for Sturm–Liouville Dynamic Equations with Deviating Arguments
by Taher S. Hassan, Clemente Cesarano, Loredana Florentina Iambor, Amir Abdel Menaem, Naveed Iqbal and Akbar Ali
Mathematics 2024, 12(10), 1532; https://doi.org/10.3390/math12101532 - 14 May 2024
Viewed by 1136
Abstract
The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales [...] Read more.
The aim of this study is to refine the known Riccati transformation technique to provide new oscillation criteria for solutions to second-order dynamic equations over time. It is important to note that the convergence or divergence of some improper integrals on time scales depends not only on the integration function but also on the integration time scale. Therefore, there has been a motivation to find new oscillation criteria that can be applicable regardless of whether ∫ζ0∞Δξa(ξ) is convergent or divergent, in contrast to what has been followed in most previous works in the literature. We have provided an example to illustrate the significance of the obtained results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena, 2nd Edition)
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