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Symmetry
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Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal...
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Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (15 August 2022) | Viewed by 17250

Special Issue Editor

Dr. Ioannis Dassios

E-Mail Website
Guest Editor
School of Electrical and Electronic Engineering, University College Dublin, D04 V1W8 Dublin, Ireland
Interests: differential/difference equations; dynamical systems; modeling and stability analysis of electric power systems; mathematics of networks; fractional calculus; mathematical modeling (power systems, materials science, energy, macroeconomics, social media, etc.); optimization for the analysis of large-scale data sets; fluid mechanics; discrete calculus; Bayes control; e-learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims at collecting the latest results related to Discrete Dynamical Systems, Mathematics of Networks, Optimization, and their application in the mathematical modeling of Signals.

This Special Issue will accept high-quality papers having original research results, and its purpose is to bring together Mathematicians with Engineers, as well as other scientists.

Topics to be covered included but are not limited to:

  • Differential/difference equations;
  • Partial differential equations;
  • Dynamical systems;
  • Mathematics of networks;
  • Fractional calculus;
  • Modelling and stability analysis of signal models;
  • Discrete calculus;
  • Circuits theory;
  • Signal processing.

You may choose our Joint Special Issue in Signals.

Prof. Dr. Ioannis Dassios
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • Differential/difference equations
  • Partial differential equations
  • Dynamical systems
  • Mathematics of networks
  • Fractional calculus
  • Modelling and stability analysis of signal models
  • Discrete calculus
  • Circuits theory
  • Signal processing

Published Papers (9 papers)

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Research

11 pages, 966 KiB  
Article
Interpolating Scaling Functions Tau Method for Solving Space–Time Fractional Partial Differential Equations
by Haifa Bin Jebreen and Carlo Cattani
Symmetry 2022, 14(11), 2463; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14112463 - 21 Nov 2022
Cited by 1 | Viewed by 1169
Abstract
This paper is devoted to an innovative and efficient technique for solving space–time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that the bases used are interpolating scaling functions (ISFs). The operational metrics for the derivative operator and [...] Read more.
This paper is devoted to an innovative and efficient technique for solving space–time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that the bases used are interpolating scaling functions (ISFs). The operational metrics for the derivative operator and fractional integration operator are used to introduce the operational matrix for the Caputo fractional derivative. Due to some characteristics of ISFs, such as interpolation, computation costs can be significantly reduced. We investigate the convergence of the technique, and some numerical implementations show that the method is effective for solving such equations. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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21 pages, 5739 KiB  
Article
An Efficient Technique to Solve Time-Fractional Kawahara and Modified Kawahara Equations
by Pavani Koppala and Raghavendar Kondooru
Symmetry 2022, 14(9), 1777; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14091777 - 26 Aug 2022
Cited by 5 | Viewed by 1193
Abstract
In this article, we analysed the approximate solutions of the time-fractional Kawahara equation and modified Kawahara equation, which describe the propagation of signals in transmission lines and the formation of nonlinear water waves in the long wavelength region. An efficient technique, namely the [...] Read more.
In this article, we analysed the approximate solutions of the time-fractional Kawahara equation and modified Kawahara equation, which describe the propagation of signals in transmission lines and the formation of nonlinear water waves in the long wavelength region. An efficient technique, namely the natural transform decomposition method, is used in the present study. Fractional derivatives are considered in Caputo, Caputo–Fabrizio, and Atangana–Baleanu operative in the Caputo manner. We have presented numerical results graphically to demonstrate the applicability and efficiency of derivatives with fractional order to depict the water waves in long wavelength regions. The symmetry pattern is a fundamental feature of the Kawahara equation and the symmetrical aspect of the solution can be seen from the graphical representations. The obtained outcomes of the proposed method are compared to those of other well-known numerical techniques, such as the homotopy analysis method and residual power series method. Numerical solutions converge to the exact solution of the Kawahara equations, demonstrating the significance of our proposed method. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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13 pages, 3342 KiB  
Article
Approximate Solutions for a Class of Predator–Prey Systems with Nonstandard Finite Difference Schemes
by Kamsing Nonlaopon, Mohammad Mehdizadeh Khalsaraei, Ali Shokri and Maryam Molayi
Symmetry 2022, 14(8), 1660; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081660 - 11 Aug 2022
Cited by 1 | Viewed by 1228
Abstract
In this paper, we construct new nonstandard finite difference schemes to approximate a set of positive solutions for the predator–prey model, which contains different functional responses. The organization of the denominator of the discrete derivative and nonlocal approximations of nonlinear terms are employed [...] Read more.
In this paper, we construct new nonstandard finite difference schemes to approximate a set of positive solutions for the predator–prey model, which contains different functional responses. The organization of the denominator of the discrete derivative and nonlocal approximations of nonlinear terms are employed to design the new schemes. The approach results in significant qualitative improvements in how the numerical solution behaves. We establish that the proposed nonstandard finite difference methods are elementary stable and satisfy the positivity requirement. In addition, the instances of applying PESN methods to some predator–prey systems using the Beddington–DeAngelis and Nicholson–Bailey functional responses are provided here. Finally, some numerical comparisons are presented to illustrate our findings. Our results indicate that the proposed methods are very suitable for the symmetric model of predator–prey. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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15 pages, 491 KiB  
Article
Motion along a Space Curve with a Quasi-Frame in Euclidean 3-Space: Acceleration and Jerk
by Ahmed M. Elshenhab, Osama Moaaz, Ioannis Dassios and Ayman Elsharkawy
Symmetry 2022, 14(8), 1610; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081610 - 04 Aug 2022
Cited by 5 | Viewed by 1289
Abstract
The resolution of the acceleration and jerk vectors of a particle moving on a space curve in the Euclidean 3-space is considered. By applying this resolution and Siacci’s theorem, alternative resolutions of acceleration and jerk vectors are derived based on the quasi-frame. In [...] Read more.
The resolution of the acceleration and jerk vectors of a particle moving on a space curve in the Euclidean 3-space is considered. By applying this resolution and Siacci’s theorem, alternative resolutions of acceleration and jerk vectors are derived based on the quasi-frame. In the osculating plane, the acceleration vector is resolved as the sum of its tangential and radial components. In addition, in the osculating and rectifying planes, the jerk vector is resolved along the tangential direction and two special radial directions. The maximum permissible speed on a space curve at all trajectory points is established via the jerk vector formula. Finally, some examples are presented to illustrate how the results work. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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24 pages, 870 KiB  
Article
Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators
by Azzh Saad Alshehry, Muhammad Imran, Adnan Khan, Rasool Shah and Wajaree Weera
Symmetry 2022, 14(7), 1463; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14071463 - 18 Jul 2022
Cited by 38 | Viewed by 1782
Abstract
In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for [...] Read more.
In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining the approximate analytical solution of the fractional Kuramoto–Sivashinsky equation (FKS). The proposed method gives a series form solution which converges quickly towards the exact solution. To show the accuracy of the proposed method, we examine three different cases. We presented proposed method results by means of graphs and tables to ensure proposed method validity. Further, the behavior of the achieved results for the fractional order is also presented. The results we obtain by implementing the proposed method shows that our technique is extremely efficient and simple to investigate the behaviour of nonlinear models found in science and technology. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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20 pages, 1733 KiB  
Article
A New Analysis of Fractional-Order Equal-Width Equations via Novel Techniques
by Muhammad Naeem, Ahmed M. Zidan, Kamsing Nonlaopon, Muhammad I. Syam, Zeyad Al-Zhour and Rasool Shah
Symmetry 2021, 13(5), 886; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13050886 - 17 May 2021
Cited by 35 | Viewed by 3063
Abstract
In this paper, the new iterative transform method and the homotopy perturbation transform method was used to solve fractional-order Equal-Width equations with the help of Caputo-Fabrizio. This method combines the Laplace transform with the new iterative transform method and the homotopy perturbation method. [...] Read more.
In this paper, the new iterative transform method and the homotopy perturbation transform method was used to solve fractional-order Equal-Width equations with the help of Caputo-Fabrizio. This method combines the Laplace transform with the new iterative transform method and the homotopy perturbation method. The approximate results are calculated in the series form with easily computable components. The fractional Equal-Width equations play an essential role in describe hydromagnetic waves in cold plasma. Our object is to study the nonlinear behaviour of the plasma system and highlight the critical points. The techniques are very reliable, effective, and efficient, which can solve a wide range of problems arising in engineering and sciences. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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13 pages, 494 KiB  
Article
Numerical Investigation of Time-Fractional Equivalent Width Equations That Describe Hydromagnetic Waves
by Nehad Ali Shah, Ioannis Dassios and Jae Dong Chung
Symmetry 2021, 13(3), 418; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030418 - 05 Mar 2021
Cited by 14 | Viewed by 1650
Abstract
The present research article is related to the analytical investigation of some fractional-order equal-width equations. The homotopy perturbation technique along with Elzaki transformation is implemented to discuss the fractional view analysis of equal-width equations. For better understanding of the proposed procedure some examples [...] Read more.
The present research article is related to the analytical investigation of some fractional-order equal-width equations. The homotopy perturbation technique along with Elzaki transformation is implemented to discuss the fractional view analysis of equal-width equations. For better understanding of the proposed procedure some examples related to equal-width equations are presented. The identical behavior of the derived and actual solutions is observed. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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12 pages, 809 KiB  
Article
A Decomposition Method for a Fractional-Order Multi-Dimensional Telegraph Equation via the Elzaki Transform
by Nehad Ali Shah, Ioannis Dassios and Jae Dong Chung
Symmetry 2021, 13(1), 8; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010008 - 23 Dec 2020
Cited by 16 | Viewed by 2123
Abstract
In this article, the Elzaki decomposition method is used to evaluate the solution of fractional-order telegraph equations. The approximate analytical solution is obtained within the Caputo derivative operator. The examples are provided as a solution to illustrate the feasibility of the proposed methodology. [...] Read more.
In this article, the Elzaki decomposition method is used to evaluate the solution of fractional-order telegraph equations. The approximate analytical solution is obtained within the Caputo derivative operator. The examples are provided as a solution to illustrate the feasibility of the proposed methodology. The result of the proposed method and the exact solution is shown and analyzed with figures help. The analytical strategy generates the series form solution, with less computational work and a fast convergence rate to the exact solutions. The obtained results have shown a useful and straightforward procedure to analyze the problems in related areas of science and technology. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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15 pages, 782 KiB  
Article
On the Statistical GARCH Model for Managing the Risk by Employing a Fat-Tailed Distribution in Finance
by H. Viet Long, H. Bin Jebreen, I. Dassios and D. Baleanu
Symmetry 2020, 12(10), 1698; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12101698 - 15 Oct 2020
Cited by 7 | Viewed by 2632
Abstract
The Conditional Value-at-Risk (CVaR) is a coherent measure that evaluates the risk for different investing scenarios. On the other hand, since the extreme value distribution has been revealed to furnish better financial and economical data adjustment in contrast to the well-known normal distribution, [...] Read more.
The Conditional Value-at-Risk (CVaR) is a coherent measure that evaluates the risk for different investing scenarios. On the other hand, since the extreme value distribution has been revealed to furnish better financial and economical data adjustment in contrast to the well-known normal distribution, we here employ this distribution in investigating explicit formulas for the two common risk measures, i.e., VaR and CVaR, to have better tools in risk management. The formulas are then employed under the generalized autoregressive conditional heteroskedasticity (GARCH) model for risk management as our main contribution. To confirm the theoretical discussions of this work, the daily returns of several stocks are considered and worked out. The simulation results uphold the superiority of our findings. Full article
(This article belongs to the Special Issue Methods on Discrete Dynamical Systems, Networks, and Optimization for Signal Modelling)
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