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Mathematics
Special Issues
Recent Advances in Delay Differential and Difference Equations
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Recent Advances in Delay Differential and Difference Equations

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (30 June 2021) | Viewed by 9125

Special Issue Editor

Prof. Dr. Ferenc Hartung

E-Mail Website
Guest Editor
Department of Mathematics, University of Pannonia, P.O. Box 158, Egyetem u. 10., H-8201 Veszprém, Hungary
Interests: functional differential equations; state-dependent delays; numerical approximation

Special Issue Information

Dear Colleagues

Delay differential and difference equations are frequently used as mathematical models in various fields of physics, engineering, economics, and biology. The topics of this Special Issue include recent qualitative and quantitative results of this field in a broad sense. They include discrete and continuous dynamical systems, differential equations with state-dependent delays, neutral differential equations, integro-differential equations, stochastic differential and difference equations, numerical simulations of the solutions, as well as applications related to the previous classes of equations. Some possible research topics are listed in the keywords.

Prof. Dr. Ferenc Hartung
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.

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Keywords

  • Delay differential and difference equations
  • Discrete and continuous dynamical systems
  • Advanced argument
  • Applications
  • Asymptotic behavior
  • Bifurcations
  • Control
  • Numerical simulation
  • Oscillation
  • Parameter estimation
  • Periodic solutions
  • Population models
  • Positive solutions
  • Stability

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Published Papers (4 papers)

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Research

10 pages, 764 KiB  
Article
Oscillatory Solutions to Neutral Delay Differential Equations
by Fahad Alsharari, Omar Bazighifan, Taher A. Nofal, Khaled Mohamed Khedher and Youssef N. Raffoul
Mathematics 2021, 9(7), 714; https://doi.org/10.3390/math9070714 - 25 Mar 2021
Cited by 1 | Viewed by 2159
Abstract
This article aims to mark out new conditions for oscillation of the even-order Emden–Fowler neutral delay differential equations with neutral term [...] Read more.
This article aims to mark out new conditions for oscillation of the even-order Emden–Fowler neutral delay differential equations with neutral term β1ıΦα[ζr−1ı]′+β3ıΦα[ςξı]=0. The obtained results extend, and simplify known conditions in the literature. The results are illustrated with examples. Full article
(This article belongs to the Special Issue Recent Advances in Delay Differential and Difference Equations)
12 pages, 575 KiB  
Article
Non-Spiking Laser Controlled by a Delayed Feedback
by Anton V. Kovalev, Evgeny A. Viktorov and Thomas Erneux
Mathematics 2020, 8(11), 2069; https://doi.org/10.3390/math8112069 - 20 Nov 2020
Viewed by 1935
Abstract
In 1965, Statz et al. (J. Appl. Phys. 30, 1510 (1965)) investigated theoretically and experimentally the conditions under which spiking in the laser output can be completely suppressed by using a delayed optical feedback. In order to explore its effects, they formulate a [...] Read more.
In 1965, Statz et al. (J. Appl. Phys. 30, 1510 (1965)) investigated theoretically and experimentally the conditions under which spiking in the laser output can be completely suppressed by using a delayed optical feedback. In order to explore its effects, they formulate a delay differential equation model within the framework of laser rate equations. From their numerical simulations, they concluded that the feedback is effective in controlling the intensity laser pulses provided the delay is short enough. Ten years later, Krivoshchekov et al. (Sov. J. Quant. Electron. 5394 (1975)) reconsidered the Statz et al. delay differential equation and analyzed the limit of small delays. The stability conditions for arbitrary delays, however, were not determined. In this paper, we revisit Statz et al.’s delay differential equation model by using modern mathematical tools. We determine an asymptotic approximation of both the domains of stable steady states as well as a sub-domain of purely exponential transients. Full article
(This article belongs to the Special Issue Recent Advances in Delay Differential and Difference Equations)
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34 pages, 548 KiB  
Article
Analysis of the Sign of the Solution for Certain Second-Order Periodic Boundary Value Problems with Piecewise Constant Arguments
by Sebastián Buedo-Fernández, Daniel Cao Labora, Rosana Rodríguez-López and Stepan A. Tersian
Mathematics 2020, 8(11), 1953; https://doi.org/10.3390/math8111953 - 4 Nov 2020
Cited by 1 | Viewed by 1965
Abstract
We find sufficient conditions for the unique solution of certain second-order boundary value problems to have a constant sign. To this purpose, we use the expression in terms of a Green’s function of the unique solution for impulsive linear periodic boundary value problems [...] Read more.
We find sufficient conditions for the unique solution of certain second-order boundary value problems to have a constant sign. To this purpose, we use the expression in terms of a Green’s function of the unique solution for impulsive linear periodic boundary value problems associated with second-order differential equations with a functional dependence, which is a piecewise constant function. Our analysis lies in the study of the sign of the Green’s function. Full article
(This article belongs to the Special Issue Recent Advances in Delay Differential and Difference Equations)
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21 pages, 328 KiB  
Article
Jump Models with Delay—Option Pricing and Logarithmic Euler–Maruyama Scheme
by Nishant Agrawal and Yaozhong Hu
Mathematics 2020, 8(11), 1932; https://doi.org/10.3390/math8111932 - 2 Nov 2020
Cited by 5 | Viewed by 2062
Abstract
In this paper, we obtain the existence, uniqueness, and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market and the Black–Scholes formula for [...] Read more.
In this paper, we obtain the existence, uniqueness, and positivity of the solution to delayed stochastic differential equations with jumps. This equation is then applied to model the price movement of the risky asset in a financial market and the Black–Scholes formula for the price of European option is obtained together with the hedging portfolios. The option price is evaluated analytically at the last delayed period by using the Fourier transformation technique. However, in general, there is no analytical expression for the option price. To evaluate the price numerically, we then use the Monte-Carlo method. To this end, we need to simulate the delayed stochastic differential equations with jumps. We propose a logarithmic Euler–Maruyama scheme to approximate the equation and prove that all the approximations remain positive and the rate of convergence of the scheme is proved to be 0.5. Full article
(This article belongs to the Special Issue Recent Advances in Delay Differential and Difference Equations)
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