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Mathematics
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Modeling and Simulation in Dynamical Systems
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Modeling and Simulation in Dynamical Systems

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 6430

Special Issue Editors

Prof. Dr. Saulius Minkevičius

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Guest Editor
Department of Mathematics and informatics Institute, Vilnius University, 01513 Vilnius, Lithuania
Interests: operations research; queueing theory; dynamical systems
Prof. Dr. Leonidas Sakalauskas

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Guest Editor
Institute of Data Science & Digital Technologies, Vilnius University, 01513 Vilnius, Italy
Interests: optimization; data mining and knowledge discovery; simulation; algorithms; modeling; probability
Prof. Dr. Darius Plikynas

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Guest Editor
Institute of data science and digital technologies (VU) and Business technologies department at VGTU, Vilnius University (VU) and Vilnius Gediminas Technical University (VGTU), 01513 Vilnius, Italy
Interests: machine learning; image processing; computational intelligence; artificial intelligence; neural networks; evolutionary computation; soft computing

Special Issue Information

Dear Colleagues,

I invite you to actively participate in a Special Issue of the journal, which will be devoted to the study of scientific problems in dynamical theory.

The dynamical system concept is a mathematical formalization for any fixed "rule" that describes the time dependence of a point's position in its ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each spring in a lake. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space. Small changes in the state of the system correspond to small changes in the numbers. The numbers are also the coordinates of a geometrical space—a manifold. The evolution rule of the dynamical system is a fixed rule that describes what future states follow from the current state. The rule may be deterministic (for a given time interval one future state can be precisely predicted given the current state) or stochastic (the evolution of the state can only be predicted with a certain probability). Related fields are Arithmetic dynamics, Chaos theory, Complex systems, Control theory, Ergodic theory, Functional analysis, Graph dynamical systems, Projected dynamical systems, Symbolic dynamics, System dynamics, and Topological dynamics. Applications are in biomechanics, in cognitive science, in second language development.

Prof. Dr. Saulius Minkevičius
Prof. Dr. Leonidas Sakalauskas
Prof. Dr. Darius Plikynas
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

  • operation research
  • cognitive science
  • probability
  • optimization
  • modeling and simulation

Published Papers (4 papers)

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Research

21 pages, 987 KiB  
Article
Numerical Methods That Preserve a Lyapunov Function for Ordinary Differential Equations
by Yadira Hernández-Solano and Miguel Atencia
Mathematics 2023, 11(1), 71; https://doi.org/10.3390/math11010071 - 25 Dec 2022
Cited by 2 | Viewed by 1395
Abstract
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is implemented for the numerical integration of a system [...] Read more.
The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e., numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is implemented for the numerical integration of a system of ordinary differential equations. In principle, this procedure yields first-order methods, but the analysis paves the way for the design of higher-order methods. As a case in point, the proposed method is applied to the Duffing equation without external forcing, considering that, in this case, preserving the Lyapunov function is more important than the accuracy of particular trajectories. Results are validated by means of numerical experiments, where the discrete gradient method is compared to standard Runge–Kutta methods. As predicted by the theory, discrete gradient methods preserve the Lyapunov function, whereas conventional methods fail to do so, since either periodic solutions appear or the energy does not decrease. Moreover, the discrete gradient method outperforms conventional schemes when these do preserve the Lyapunov function, in terms of computational cost; thus, the proposed method is promising. Full article
(This article belongs to the Special Issue Modeling and Simulation in Dynamical Systems)
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23 pages, 1597 KiB  
Article
Framework for Integrated Use of Agent-Based and Ambient-Oriented Modeling
by Khurrum Mustafa Abbasi, Tamim Ahmed Khan and Irfan ul Haq
Mathematics 2022, 10(21), 4157; https://doi.org/10.3390/math10214157 - 07 Nov 2022
Cited by 3 | Viewed by 1665
Abstract
Agent-based modeling (ABM) is a flexible and simulation-friendly modeling approach. Ambient-oriented modeling is effective for systems containing ambient and spatial representations. In this paper we propose a framework for the integrated use of agent-based modeling and ambient-oriented modeling. We analyze both agents and [...] Read more.
Agent-based modeling (ABM) is a flexible and simulation-friendly modeling approach. Ambient-oriented modeling is effective for systems containing ambient and spatial representations. In this paper we propose a framework for the integrated use of agent-based modeling and ambient-oriented modeling. We analyze both agents and ambient in detail. We also compare both modeling approaches as well and analyze their similarities and differences. The integrated implementation provides a new link between mathematical modeling and simulations. The model developed using this framework has four parts. The first part constitutes the identification, definition, and relations of agents. In this part, we use agent-based modeling along with the concepts of discrete-event simulations and system dynamics. The second part of the model is the mathematical representation of the relations of agents, i.e., the parent and child relation of agents. The third part of the model is the representation of the messages along with relational symbols where we utilize the concepts and symbols of relations and messages from ambient-oriented modeling. The fourth and final part of the model is the simulation, where we describe the rules that govern the processes represented in first two parts. The framework is helpful in overcoming certain limitations of both approaches. Moreover, we provide a scenario of a bus rapid transit system (BRTS) as a proof of concept, and we examine the generic concept of BRTSs using the proposed framework. Full article
(This article belongs to the Special Issue Modeling and Simulation in Dynamical Systems)
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22 pages, 6383 KiB  
Article
Causal Interactions in Agile Application Development
by Saulius Gudas and Karolis Noreika
Mathematics 2022, 10(9), 1497; https://doi.org/10.3390/math10091497 - 30 Apr 2022
Cited by 1 | Viewed by 1531
Abstract
The Agile approach and tools are popular for the management of Enterprise Application Software (EAS) development. This article focuses on the issue of inconsistency between strategic business objectives and the functionality of the software developed. Agile management tools lack the functionality of EAS [...] Read more.
The Agile approach and tools are popular for the management of Enterprise Application Software (EAS) development. This article focuses on the issue of inconsistency between strategic business objectives and the functionality of the software developed. Agile management tools lack the functionality of EAS project activities coordination. This article aims to rethink Agile project management using the causal modelling approach. A causal model of Agile project management using a management transaction (MT) concept was developed. The notion of the space of processes was used to identify the MTs location along the axes of aggregation, generalization, and time and to formalize their interaction specifications. Taxonomy of the coordination meta-types and types was developed using the identifiers of the MTs. The modified Agile activities hierarchy was developed, and vertical and horizontal causal interactions between Agile activities were identified. This modified Agile management model helps to consistently track the integrity of EAS project content. Complexity indicators were introduced to evaluate the EAS project complexity and their average and normalized values are presented. Additional attributes in the Agile management tool Jira are proposed. Monitoring mismatch between strategic business objectives and development activities content helps to improve the success of EAS projects delivery. Full article
(This article belongs to the Special Issue Modeling and Simulation in Dynamical Systems)
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18 pages, 341 KiB  
Article
Diversity of Bivariate Concordance Measures
by Martynas Manstavičius
Mathematics 2022, 10(7), 1103; https://doi.org/10.3390/math10071103 - 29 Mar 2022
Cited by 1 | Viewed by 1165
Abstract
We revisit the axioms of Scarsini, defining bivariate concordance measures for a pair of continuous random variables (X,Y); such measures can be understood as functions of the bivariate copula C associated with (X,Y). [...] Read more.
We revisit the axioms of Scarsini, defining bivariate concordance measures for a pair of continuous random variables (X,Y); such measures can be understood as functions of the bivariate copula C associated with (X,Y). Two constructions, investigated in the works of Edwards, Mikusiński, Taylor, and Fuchs, are generalized, yielding, in particular, examples of higher than degree-two polynomial-type concordance measures, along with examples of non-polynomial-type concordance measures, and providing an incentive to investigate possible further characterizations of such concordance measures, as was achieved by Edwards and Taylor for the degree-one case. Full article
(This article belongs to the Special Issue Modeling and Simulation in Dynamical Systems)
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