Mathematical Modeling and Simulation of Oscillatory Phenomena

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 18546

Special Issue Editors


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

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

E-Mail Website
Guest Editor
School of Basic Sciences, Indian Institute of Technology Mandi, Mandi 175001, H.P., India
Interests: time scale calculus; delay differential equations; ecological modelling; stochastic control; difference equation

E-Mail Website
Guest Editor
Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12613, Egypt
Interests: qualitative theory; ordinary differential equations; functional differential equations; dynamical systems; mathematical modeling in physical/social/life sciences

Special Issue Information

Dear Colleagues,

Oscillatory phenomena have been observed in many dynamical systems encountered in natural sciences and technology. Much of physiology operates in an oscillatory manner, including in the examples of hormone oscillations, oscillatory gene expressions, and oscillation in muscles; oscillation processes are also observed in ecosystem populations, biochemistry, mechanics, population dynamics and there are thermodynamic oscillations, oscillations in market economies, and so on. The application prospects facilitate rapid development of the corresponding theoretical framework, generally known as oscillation theory. The problem of studying the oscillatory properties of solutions and revealing their relationship with corresponding oscillatory processes in systems of a diversified physical nature is still a subject of intensive research.

This Special Issue focuses on the modeling and simulation of nonlinear dynamical systems of various nature that exhibit oscillation as their fundamental mode of behavior.

Papers are invited from those who work on oscillation theory or in any one of the areas in which existing tools and methods are applied to investigate the oscillatory phenomena of a given dynamical system modeling a real-world problem. Having in mind that the delay is one of the major causes of oscillations in dynamical systems, we are particularly interested in (but not exclusively) the oscillation theory of time-delay systems.

We look forward to receiving your submissions.

Dr. Irena Jadlovská
Prof. Dr. Tongxing Li
Prof. Dr. Syed Abbas
Prof. Dr. Said R Grace
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

Related Special Issue

Published Papers (17 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

9 pages, 263 KiB  
Article
New Criteria of Oscillation for Linear Sturm–Liouville Delay Noncanonical Dynamic Equations
by Taher S. Hassan, Martin Bohner, Iambor Loredana Florentina, Amir Abdel Menaem and Mouataz Billah Mesmouli
Mathematics 2023, 11(23), 4850; https://doi.org/10.3390/math11234850 - 01 Dec 2023
Cited by 2 | Viewed by 687
Abstract
In this work, we deduce a new criterion that guarantees the oscillation of solutions to linear Sturm–Liouville delay noncanonical dynamic equations; these results emulate the criteria of the Hille and Ohriska types for canonical dynamic equations, and these results also solve an open [...] Read more.
In this work, we deduce a new criterion that guarantees the oscillation of solutions to linear Sturm–Liouville delay noncanonical dynamic equations; these results emulate the criteria of the Hille and Ohriska types for canonical dynamic equations, and these results also solve an open problem in many works in the literature. Several examples are offered, demonstrating that the findings achieved are precise, practical, and adaptable. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
16 pages, 7770 KiB  
Communication
Chaotic Vibration and Perforation Effects on the Sound Absorption of a Nonlinear Curved Panel Absorber
by Yiu-Yin Lee
Mathematics 2023, 11(14), 3178; https://doi.org/10.3390/math11143178 - 20 Jul 2023
Cited by 1 | Viewed by 579
Abstract
This study is the first to investigate the effect of chaotic vibration on the sound absorption of a curved perforated panel. Previous studies on the effect of nonlinear vibration on the sound absorption of a panel absorber have focused on periodic responses only. [...] Read more.
This study is the first to investigate the effect of chaotic vibration on the sound absorption of a curved perforated panel. Previous studies on the effect of nonlinear vibration on the sound absorption of a panel absorber have focused on periodic responses only. In this study, a sound absorption formula was derived by considering the panel impedance and perforation impedance. The numerical integration method was adopted to generate various chaotic vibrational responses, which were used to compute the corresponding sound absorptions. Several interesting findings that have never been observed in any previous studies on acoustic absorption were derived. First, in the chaotic and highly nonlinear cases, as the excitation frequency increased, the corresponding response frequencies decreased. This was opposite to the typical trend in linear cases, in which higher excitation frequencies corresponded to higher response frequencies. Second, in chaotic cases, absorption mainly occurred due to panel vibration effects. This is also in stark contrast to the findings of studies on perforated vibrating panels, in which the absorption effect mainly originates from perforations. Additionally, the absorption bandwidths are much wider and can shift to higher frequencies; however, the peak absorption coefficients were approximately 20% lower than in the case of the perforation effect only. Third, in the quasi-chaotic case, the absorption curve in the case of the perforation effect plus the vibration effect was between the absorption curves of the perforation effect only and the perforation effect plus the vibration effect. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

13 pages, 13982 KiB  
Article
Chaotic States of Transistor-Based Tuned-Collector Oscillator
by Jiri Petrzela
Mathematics 2023, 11(9), 2213; https://doi.org/10.3390/math11092213 - 08 May 2023
Cited by 2 | Viewed by 851
Abstract
This brief paper shows that robust chaotic behavior can be detected within a tuned-collector single-stage transistor-based oscillator. The content of this work also contributes to the problem of chaos localization in simplified mathematical model of standard analog building block. Searching for chaos is [...] Read more.
This brief paper shows that robust chaotic behavior can be detected within a tuned-collector single-stage transistor-based oscillator. The content of this work also contributes to the problem of chaos localization in simplified mathematical model of standard analog building block. Searching for chaos is performed via numerical optimization routine applied onto the principal schematic of oscillator where generalized bipolar transistor is modelled as a two-port described by impedance as well as admittance matrix. In both cases, the presence of dense chaotic attractor is proved via calculation of the largest Lyapunov exponent, while its structural stability is validated by real measurement, i.e., visualization of captured oscilloscope screenshots. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

9 pages, 4541 KiB  
Article
Canards Oscillations, Noise-Induced Splitting of Cycles and Transition to Chaos in Thermochemical Kinetics
by Irina Bashkirtseva, Grigoriy Ivanenko, Dmitrii Mordovskikh and Lev Ryashko
Mathematics 2023, 11(8), 1918; https://doi.org/10.3390/math11081918 - 19 Apr 2023
Cited by 1 | Viewed by 700
Abstract
We study how noise generates complex oscillatory regimes in the nonlinear thermochemical kinetics. In this study, the basic mathematical Zeldovich–Semenov model is used as a deterministic skeleton. We investigate the stochastic version of this model that takes into account multiplicative random fluctuations of [...] Read more.
We study how noise generates complex oscillatory regimes in the nonlinear thermochemical kinetics. In this study, the basic mathematical Zeldovich–Semenov model is used as a deterministic skeleton. We investigate the stochastic version of this model that takes into account multiplicative random fluctuations of temperature. In our study, we use direct numerical simulation of stochastic solutions with the subsequent statistical analysis of probability densities and Lyapunov exponents. In the parametric zone of Canard cycles, qualitative effects caused by random noise are identified and investigated. Stochastic P-bifurcations corresponding to noise-induced splitting of Canard oscillations are parametrically described. It is shown that such P-bifurcations are associated with splitting of both amplitudes and frequencies. Studying stochastic D-bifurcations, we localized the rather narrow parameter zone where transitions from order to chaos occur. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

10 pages, 279 KiB  
Article
Oscillation Criteria for Advanced Half-Linear Differential Equations of Second Order
by Taher S. Hassan, Qingkai Kong and Bassant M. El-Matary
Mathematics 2023, 11(6), 1385; https://doi.org/10.3390/math11061385 - 13 Mar 2023
Cited by 3 | Viewed by 939
Abstract
In this paper, we find new oscillation criteria for second-order advanced functional half-linear differential equations. Our results extend and improve recent criteria for the same equations established previously by several authors and cover the existing classical criteria for related ordinary differential equations. We [...] Read more.
In this paper, we find new oscillation criteria for second-order advanced functional half-linear differential equations. Our results extend and improve recent criteria for the same equations established previously by several authors and cover the existing classical criteria for related ordinary differential equations. We give some examples to illustrate the significance of the obtained results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
10 pages, 273 KiB  
Article
Asymptotic Behavior and Oscillation of Third-Order Nonlinear Neutral Differential Equations with Mixed Nonlinearities
by Taher S. Hassan and Bassant M. El-Matary
Mathematics 2023, 11(2), 424; https://doi.org/10.3390/math11020424 - 13 Jan 2023
Viewed by 856
Abstract
In this paper, we investigate the asymptotic properties of third-order nonlinear neutral differential equations with mixed nonlinearities using the comparison principle. Our results not only vastly improve upon but also broadly generalize many previously known ones. Examples demonstrating the applicability and efficacy of [...] Read more.
In this paper, we investigate the asymptotic properties of third-order nonlinear neutral differential equations with mixed nonlinearities using the comparison principle. Our results not only vastly improve upon but also broadly generalize many previously known ones. Examples demonstrating the applicability and efficacy of our results are provided. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
14 pages, 453 KiB  
Article
New Explicit Oscillation Criteria for First-Order Differential Equations with Several Non-Monotone Delays
by Emad Attia and Bassant El-Matary
Mathematics 2023, 11(1), 64; https://doi.org/10.3390/math11010064 - 24 Dec 2022
Cited by 1 | Viewed by 1010
Abstract
The oscillation of a first-order differential equation with several non-monotone delays is proposed. We extend the works of Kwong (1991) and Sficas and Stavroulakis (2003) for equations with several delays. Our results not only essentially improve but also generalize a large number of [...] Read more.
The oscillation of a first-order differential equation with several non-monotone delays is proposed. We extend the works of Kwong (1991) and Sficas and Stavroulakis (2003) for equations with several delays. Our results not only essentially improve but also generalize a large number of the existing ones. Using some numerical examples, we illustrate the applicability and effectiveness of our results over many known results in the literature. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

13 pages, 723 KiB  
Article
Closed-Form Solutions to a Forced Damped Rotational Pendulum Oscillator
by Alvaro H. Salas, Ma’mon Abu Hammad, Badriah M. Alotaibi, Lamiaa S. El-Sherif and Samir A. El-Tantawy
Mathematics 2022, 10(21), 4000; https://doi.org/10.3390/math10214000 - 28 Oct 2022
Cited by 3 | Viewed by 1095
Abstract
In this investigation, some analytical solutions to both conserved and non-conserved rotational pendulum systems are reported. The exact solution to the conserved oscillator (unforced, undamped rotational pendulum oscillator), is derived in the form of a Jacobi elliptical function. Moreover, an approximate solution for [...] Read more.
In this investigation, some analytical solutions to both conserved and non-conserved rotational pendulum systems are reported. The exact solution to the conserved oscillator (unforced, undamped rotational pendulum oscillator), is derived in the form of a Jacobi elliptical function. Moreover, an approximate solution for the conserved case is obtained in the form of a trigonometric function. A comparison between both exact and approximate solutions to the conserved oscillator is examined. Moreover, the analytical approximations to the non-conserved oscillators including the unforced, damped rotational pendulum oscillator and forced, damped rotational pendulum oscillator are obtained. Furthermore, all mentioned oscillators (conserved and non-conserved oscillators) are linearized, and their exact solutions are derived. In addition, all obtained approximations are compared with the four-order Runge–Kutta (RK4) numerical approximations and with the exact solutions to the linearized oscillators. The obtained results can help several authors for discussing and interpreting their results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

18 pages, 326 KiB  
Article
Improved Hille-Type Oscillation Criteria for Second-Order Quasilinear Dynamic Equations
by Taher S. Hassan, Clemente Cesarano, Rami Ahmad El-Nabulsi and Waranont Anukool
Mathematics 2022, 10(19), 3675; https://doi.org/10.3390/math10193675 - 07 Oct 2022
Cited by 5 | Viewed by 885
Abstract
In this work, we develop enhanced Hille-type oscillation conditions for arbitrary-time, second-order quasilinear functional dynamic equations. These findings extend and improve previous research that has been published in the literature. Some examples are given to demonstrate the importance of the obtained results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
19 pages, 1051 KiB  
Article
Time-Optimal Control Problem of Two Non-Synchronous Oscillators
by Leonid Berlin, Andrey Galyaev and Pavel Lysenko
Mathematics 2022, 10(19), 3552; https://doi.org/10.3390/math10193552 - 29 Sep 2022
Cited by 1 | Viewed by 1032
Abstract
The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator is controlled with a shared limited scalar control. The objective of the control is to accelerate the oscillatory system to a given specific position, where the first [...] Read more.
The time-optimal control problem for a system consisting of two non-synchronous oscillators is considered. Each oscillator is controlled with a shared limited scalar control. The objective of the control is to accelerate the oscillatory system to a given specific position, where the first oscillator must have non-zero phase coordinates, but the second one must remain motionless at the terminal moment. For an arbitrary number of unknown switching moments that determine the optimal relay control, the necessary extremum conditions in the form of nonlinear matrix equalities are proposed. The study of the necessary/sufficient conditions of the extremum made it possible to describe the reachability set in the phase space of the first oscillator, to find an analytical form of the curve corresponding to the two-switching control class, which also separates the reachability set of the three switching-control class. The corresponding theorems are proved and the dependence of the criteria on control constraints is shown. Matrix conditions for different classes of control switchings are found. All of the obtained analytical results are numerically validated and illustrated with mathematical modeling. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

16 pages, 781 KiB  
Article
Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques
by Uroosa Arshad, Mariam Sultana, Ali Hasan Ali, Omar Bazighifan, Areej A. Al-moneef and Kamsing Nonlaopon
Mathematics 2022, 10(17), 3071; https://doi.org/10.3390/math10173071 - 25 Aug 2022
Cited by 14 | Viewed by 2112
Abstract
In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional [...] Read more.
In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

11 pages, 284 KiB  
Article
Some New Oscillation Results for Higher-Order Nonlinear Differential Equations with a Nonlinear Neutral Term
by John R. Graef, Said R. Grace, Irena Jadlovská and Ercan Tunç
Mathematics 2022, 10(16), 2997; https://doi.org/10.3390/math10162997 - 19 Aug 2022
Cited by 1 | Viewed by 962
Abstract
The authors study the oscillatory behaviors of solutions of higher-order nonlinear differential equations with a nonlinear neutral term. The right hand side of their equation contains both an advanced and a delay term, and either (or both) of them can be sublinear or [...] Read more.
The authors study the oscillatory behaviors of solutions of higher-order nonlinear differential equations with a nonlinear neutral term. The right hand side of their equation contains both an advanced and a delay term, and either (or both) of them can be sublinear or superlinear. The influence of these terms on the oscillatory and asymptotic behaviors of solutions is investigated by using a comparison to first-order advanced and delay differential equations. New oscillation criteria are presented that improve and extend many known oscillation criteria in the literature. An example is provided to illustrate the results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
11 pages, 256 KiB  
Article
Limit Cycles and Integrability of a Class of Quintic System
by Yanli Tang, Dongmei Zhang and Feng Li
Mathematics 2022, 10(16), 2993; https://doi.org/10.3390/math10162993 - 19 Aug 2022
Viewed by 838
Abstract
In this paper, a class of quintic systems is investigated. The first 13 focal values are computed with the aid of MATHEMATICA. Then the necessary conditions of integrability and linearizability are obtained and the sufficiency of every condition is proved. Meanwhile, bifurcation of [...] Read more.
In this paper, a class of quintic systems is investigated. The first 13 focal values are computed with the aid of MATHEMATICA. Then the necessary conditions of integrability and linearizability are obtained and the sufficiency of every condition is proved. Meanwhile, bifurcation of limit cycles is discussed, 13 limit cycles can be bifurcated from the origin. As far as the number of limit cycles enclosing an isolated singular point is concerned, this is so far the best result for elementary singular points. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
16 pages, 3269 KiB  
Article
Detection and Analysis of Critical Dynamic Properties of Oligodendrocyte Differentiation
by Svetoslav G. Nikolov, Olaf Wolkenhauer, Momchil Nenov and Julio Vera
Mathematics 2022, 10(16), 2928; https://doi.org/10.3390/math10162928 - 14 Aug 2022
Cited by 1 | Viewed by 1052
Abstract
In this paper, we derive a four-dimensional ordinary differential equation (ODE) model representing the main interactions between Sox9, Sox10, Olig2 and several miRNAs, which drive the process of (olygodendrocyte) differentiation. We utilize the Lyapunov–Andronov theory to analyze its dynamical properties. Our results indicated [...] Read more.
In this paper, we derive a four-dimensional ordinary differential equation (ODE) model representing the main interactions between Sox9, Sox10, Olig2 and several miRNAs, which drive the process of (olygodendrocyte) differentiation. We utilize the Lyapunov–Andronov theory to analyze its dynamical properties. Our results indicated that the strength of external signaling (morphogenic gradients shh and bmp), and the transcription rate of mOlig2 explain the existence of stable and unstable (sustained oscillations) behavior in the system. Possible biological implications are discussed. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

12 pages, 775 KiB  
Article
Novel Approximations to the (Un)forced Pendulum–Cart System: Ansatz and KBM Methods
by Weaam Alhejaili, Alvaro H. Salas and Samir A. El-Tantawy
Mathematics 2022, 10(16), 2908; https://doi.org/10.3390/math10162908 - 12 Aug 2022
Cited by 10 | Viewed by 993
Abstract
In the present investigation, some novel analytical approximations to both unforced and forced pendulum–cart system oscillators are obtained. In our investigation, two accurate and effective approaches, namely, the ansatz method with equilibrium point and the Krylov–Bogoliubov–Mitropolsky (KBM) method, are implemented for analyzing pendulum–cart [...] Read more.
In the present investigation, some novel analytical approximations to both unforced and forced pendulum–cart system oscillators are obtained. In our investigation, two accurate and effective approaches, namely, the ansatz method with equilibrium point and the Krylov–Bogoliubov–Mitropolsky (KBM) method, are implemented for analyzing pendulum–cart problems.The obtained results are compared with the Runge–Kutta (RK4) numerical approximation. The obtained approximations using both ansatz and KBM methods show good coincidence with RK4 numerical approximation. In addition, the global maximum error is estimated as compared to RK4 numerical approximation. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Show Figures

Figure 1

12 pages, 292 KiB  
Article
On the Asymptotic Behavior of Noncanonical Third-Order Emden–Fowler Delay Differential Equations with a Superlinear Neutral Term
by Qingmin Liu, Said R. Grace, Irena Jadlovská, Ercan Tunç and Tongxing Li
Mathematics 2022, 10(16), 2902; https://doi.org/10.3390/math10162902 - 12 Aug 2022
Cited by 2 | Viewed by 894
Abstract
The present paper is concerned with the asymptotic behavior of solutions to a class of noncanonical third-order Emden–Fowler delay differential equations with a superlinear neutral term. Using a Riccati-type transformation as well as integral criteria, we establish some new sufficient conditions guaranteeing that [...] Read more.
The present paper is concerned with the asymptotic behavior of solutions to a class of noncanonical third-order Emden–Fowler delay differential equations with a superlinear neutral term. Using a Riccati-type transformation as well as integral criteria, we establish some new sufficient conditions guaranteeing that every solution of the equation considered either oscillates or converges to zero asymptotically. The results are illustrated with two examples. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
12 pages, 280 KiB  
Article
Oscillation of Second Order Nonlinear Neutral Differential Equations
by Yingzhu Wu, Yuanhong Yu and Jinsen Xiao
Mathematics 2022, 10(15), 2739; https://doi.org/10.3390/math10152739 - 02 Aug 2022
Cited by 2 | Viewed by 957
Abstract
The study of the oscillatory behavior of solutions to second order nonlinear differential equations is motivated by their numerous applications in the natural sciences and engineering. In the presented research, some new oscillation criteria for a class of damped second order neutral differential [...] Read more.
The study of the oscillatory behavior of solutions to second order nonlinear differential equations is motivated by their numerous applications in the natural sciences and engineering. In the presented research, some new oscillation criteria for a class of damped second order neutral differential equations with noncanonical operators are established. The results extend and improve on those reported in the literature. Moreover, some examples are provided to show the significance of the results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
Back to TopTop