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Dynamical Systems and Optimal Control, 2nd Edition
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Dynamical Systems and Optimal Control, 2nd Edition

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

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 10548

Special Issue Editor

Prof. Dr. Temirkhan Aleroev

E-Mail Website
Guest Editor
Department of Applied Mathematics, National Research Moscow State University of Civil Engineering, Moscow, Russia
Interests: differential equations; dynamical systems and optimal control; applied mathematics; mathematics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The vast majority of papers in this Issue will be devoted to local and nonlocal condition and transference differential equations of heat and mass transference mathematical processes in continuous media with memory and in media with fractal structure. These papers shall investigate modified initial and mixed boundary value problems for generalized transfer differential equations of integral and fractional orders.

Additionally, some papers will be devoted to numerical schemes and an alternating direction implicit (ADI) scheme for one-dimensional and two-dimensional time-space fractional vibration equations (FVEs), respectively. Here, the considered time-space FVEs are equivalently transformed into their partial integrodifferential forms with the classical first-order integrals and the Riemann–Liouville derivative.

Prof. Dr. Temirkhan Aleroev
Guest Editor

Manuscript Submission Information

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Keywords

  • differential equation
  • boundary value problem
  • fractional derivative
  • fractional integral
  • time–space fractional vibration equation
  • convergence
  • stability
  • eigenvalue
  • eigenfunction
  • green function

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Published Papers (6 papers)

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Research

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7 pages, 260 KiB  
Article
Moving Singular Points and the Van der Pol Equation, as Well as the Uniqueness of Its Solution
by Victor Orlov
Mathematics 2023, 11(4), 873; https://doi.org/10.3390/math11040873 - 8 Feb 2023
Cited by 5 | Viewed by 1186
Abstract
The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about [...] Read more.
The article considers the Van der Pol equation nonlinearity aspect related to a moving singular point. The fact of the existence of moving singular points and the uniqueness of their solution for complex domains have been proved. An answer to the question about the existence of moving singular points in the real domain was obtained. The proof of existence and uniqueness is based on an author’s modification of the technology of the classical Cauchy theorem. A priori estimates of the analytical approximate solution in the vicinity of a moving singular point are obtained. Calculations of a numerical experiment are presented. Full article
(This article belongs to the Special Issue Dynamical Systems and Optimal Control, 2nd Edition)
13 pages, 764 KiB  
Article
Analytical and Numerical Study on Forced and Damped Complex Duffing Oscillators
by Weaam Alhejaili, Alvaro H. Salas and Samir A. El-Tantawy
Mathematics 2022, 10(23), 4475; https://doi.org/10.3390/math10234475 - 27 Nov 2022
Cited by 9 | Viewed by 1097
Abstract
In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and [...] Read more.
In this work, some general forms for forced and damped complex Duffing oscillators (FDCDOs), including two different models, which are known as the forced and damped complex Duffing oscillator (I) (FDCDO (I)) and FDCDO (II), are investigated by using some effective analytical and numerical approaches. For the analytical approximation, the two models of the FDCDOs are reduced to two decoupled standard forced and damped Duffing oscillators (FDDOs). After that, both the ansatz method and Krylov–Bogoliubov–Mitropolsky (KBM) approach are applied in order to derive some accurate analytical approximations in terms of trigonometric functions. For the numerical approximations, the finite difference method is employed to analyze the two coupled models without causing them to be decoupled for the original problems. In addition, all obtained analytical and numerical approximations are compared with the fourth-order Runge–Kutta (RK4) numerical approximations. Moreover, the maximum residual distance error (MRDE) is estimated in order to verify the accuracy of all obtained approximations. Full article
(This article belongs to the Special Issue Dynamical Systems and Optimal Control, 2nd Edition)
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11 pages, 801 KiB  
Article
Quality Evaluation for Reconstructing Chaotic Attractors
by Madalin Frunzete
Mathematics 2022, 10(22), 4229; https://doi.org/10.3390/math10224229 - 12 Nov 2022
Cited by 3 | Viewed by 1549
Abstract
Dynamical systems are used in various applications, and their simulation is related with the type of mathematical operations used in their construction. The quality of the system is evaluated in terms of reconstructing the system, starting from its final point to the beginning [...] Read more.
Dynamical systems are used in various applications, and their simulation is related with the type of mathematical operations used in their construction. The quality of the system is evaluated in terms of reconstructing the system, starting from its final point to the beginning (initial conditions). Deciphering a message has to be without loss, and this paper will serve to choose the proper dynamical system to be used in chaos-based cryptography. The characterization of the chaotic attractors is the most important information in order to obtain the desired behavior. Here, observability and singularity are the main notions to be used for introducing an original term: quality observability index (q.o.i.). This is an original contribution for measuring the quality of the chaotic attractors. In this paper, the q.o.i. is defined and computed in order to confirm its usability. Full article
(This article belongs to the Special Issue Dynamical Systems and Optimal Control, 2nd Edition)
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7 pages, 268 KiB  
Article
Technology for Obtaining the Approximate Value of Moving Singular Points for a Class of Nonlinear Differential Equations in a Complex Domain
by Victor Orlov and Magomedyusuf Gasanov
Mathematics 2022, 10(21), 3984; https://doi.org/10.3390/math10213984 - 27 Oct 2022
Cited by 6 | Viewed by 1472
Abstract
In previous studies, the authors formulated precise criteria for finding moving singular points of one class of nonlinear differential equations with a second degree polynomial right-hand side for a real domain. In this paper, the authors generalize these exact criteria to a complex [...] Read more.
In previous studies, the authors formulated precise criteria for finding moving singular points of one class of nonlinear differential equations with a second degree polynomial right-hand side for a real domain. In this paper, the authors generalize these exact criteria to a complex one by using phase spaces. The proposed technology for obtaining an approximate value of moving singular points is necessary for developing PC programs. This technology has been tested in a manual version based on a numerical experiment. Full article
(This article belongs to the Special Issue Dynamical Systems and Optimal Control, 2nd Edition)
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12 pages, 1027 KiB  
Article
Boundary Value Problem of Space-Time Fractional Advection Diffusion Equation
by Elsayed I. Mahmoud and Temirkhan S. Aleroev
Mathematics 2022, 10(17), 3160; https://doi.org/10.3390/math10173160 - 2 Sep 2022
Cited by 3 | Viewed by 1797
Abstract
In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic [...] Read more.
In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic equation is determined, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme of the equivalent partial integro-differential equations. The convergence and unconditional stability of the solution are investigated. Finally, the numerical and analytical experiments are given to verify the theoretical analysis. Full article
(This article belongs to the Special Issue Dynamical Systems and Optimal Control, 2nd Edition)
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Review

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18 pages, 5115 KiB  
Review
Mathematical Model for Analyzing the Dynamics of Tungro Virus Disease in Rice: A Systematic Literature Review
by Rika Amelia, Nursanti Anggriani, Asep K. Supriatna and Noor Istifadah
Mathematics 2022, 10(16), 2944; https://doi.org/10.3390/math10162944 - 15 Aug 2022
Cited by 5 | Viewed by 2601
Abstract
One of the main obstacles in rice cultivation is the tungro virus disease caused by Rice tungro spherical virus (RTSV) and Rice tungro bacilliform virus (RTBV). These viruses are transmitted by green leafhopper (Nephotettix virescens) vector, semi-persistently after sucking infected plants. [...] Read more.
One of the main obstacles in rice cultivation is the tungro virus disease caused by Rice tungro spherical virus (RTSV) and Rice tungro bacilliform virus (RTBV). These viruses are transmitted by green leafhopper (Nephotettix virescens) vector, semi-persistently after sucking infected plants. Subsequently, the vectors migrate and suck susceptible plants, but they can be controlled chemically and biologically. Mathematical modeling is one of the tools that can be used to analyze the spread of disease in plants. A literature review was conducted regarding the mathematical model of the spread of tungro virus disease in rice plants with the data sourced from scholarly references available in the dimension database, Google Scholar, and Scopus in 2012–2021. The steps followed include conducting a literature analysis and examining the mathematical model of the transmission of tungro virus disease in rice plants to identify gaps for future research. The results show that since 2016, few studies have analyzed mathematical models of the spread of tungro virus disease in rice plants. This is evident from the data search results, which show that only four articles were acquired through the option of duplication and visualization using VOSviewer software. Full article
(This article belongs to the Special Issue Dynamical Systems and Optimal Control, 2nd Edition)
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