Special Issue "Applied Mathematical Modelling and Dynamical Systems"

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

Deadline for manuscript submissions: 30 September 2022 | Viewed by 2895

Special Issue Editors

Prof. Dr. João Cabral
E-Mail Website
Guest Editor
Faculdade de Ciências e Tecnologia, University of Azores, 9500-321 Ponta Delgada, Portugal
Interests: rational maps iteration; dynamical systems; mathematical modeling; environment dynamics of mathematics methodology and teaching
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Daniele Fournier-Prunaret
E-Mail Website
Guest Editor
Institut National des Sciences Appliquées de Toulouse, Toulouse, France
Interests: nonlinear systems; complex behaviours; bifurcations; chaos
Prof. Dr. José Leonel Linhares da Rocha
E-Mail Website
Guest Editor
CEAUL. ADM, ISEL-Engineering Superior Institute of Lisbon, Polytechnic Institute of Lisbon, Rua Conselheiro Emídio Navarro 1, 1959-007 Lisboa, Portugal
Interests: nonlinear dynamics; population dynamics (Allee effects); bifurcation theory; networks; synchronization and applications

Special Issue Information

Dear Colleagues,

We are pleased to announce a Special Issue of the journal Mathematics entitled “Applied Mathematical Modelling and Dynamical Systems”. Many problems in our society are solved several times through the construction of little bridges connecting different branches of Mathematics. From the most theoretical aspect to the most practical equation, from the most complex nonlinear system to the most iterative process, from the most chaotical event to the most linear, great and incredible phenomena, sometimes missed when studied alone with the tools of an unique field, can be spotted when making connections between several fields, usually giving birth to amazing theories, which, when applied, produce results with the power of make human life better.

Dynamical systems can model many different phenomena in nature and society. The goal of all theoretical studies is to analyze and understand processes often related to different fields of application such as control theory, bifurcation theory, population dynamics, networks, synchronization phenomena, electronics, physics, mechanics, economics, biology, and ecology, among so many others.

This Special Issue welcomes original research articles, short communications, and review papers. Potential topics include theoretical studies as well as analyses of applied models related to all the fields cited above.

Prof. Dr. João Cabral
Prof. Dr. Daniele Fournier-Prunaret
Prof. Dr. José Leonel Linhares da Rocha
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 1800 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 modeling
  • dynamical systems
  • nonlinear systems
  • theory of singularities
  • fixed point theory
  • bifurcation theory
  • complex systems
  • iteration theory
  • topological dynamics
  • ergodic theory
  • symbolic dynamics
  • population dynamics
  • embedding problems
  • networks
  • synchronization
  • simulation
  • chaos
  • functional equations

Published Papers (5 papers)

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Research

Article
Lie Symmetry Analysis and Conservation Laws of the Axially Loaded Euler Beam
Mathematics 2022, 10(15), 2759; https://doi.org/10.3390/math10152759 - 03 Aug 2022
Viewed by 281
Abstract
By applying the Lie symmetry method, group-invariant solutions are constructed for axially loaded Euler beams. The corresponding mathematical models of the beams are formulated. After introducing the infinitesimal transformations, the determining equations of Lie symmetry are proposed via Lie point transformations acting on [...] Read more.
By applying the Lie symmetry method, group-invariant solutions are constructed for axially loaded Euler beams. The corresponding mathematical models of the beams are formulated. After introducing the infinitesimal transformations, the determining equations of Lie symmetry are proposed via Lie point transformations acting on the original equations. The infinitesimal generators of symmetries of the systems are presented with Maple. The corresponding vector fields are given to span the subalgebra of the systems. Conserved vectors are derived by using two methods, namely, the multipliers method and Noether’s theorem. Noether conserved quantities are obtained using the structure equation, satisfied by the gauge functions. The fluxes of the conservation laws could also be proposed with the multipliers. The relations between them are discussed. Furthermore, the original equations of the systems could be transformed into ODEs and the exact explicit solutions are provided. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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Article
Coexisting Attractor in a Gyrostat Chaotic System via Basin of Attraction and Synchronization of Two Nonidentical Mechanical Systems
Mathematics 2022, 10(11), 1914; https://doi.org/10.3390/math10111914 - 02 Jun 2022
Cited by 1 | Viewed by 426
Abstract
This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different [...] Read more.
This paper is divided into two main portions. First, we look at basins of attraction as a tool with a unique set of characteristics for discussing multistability and coexisting attractors in a gyrostat chaotic system. For the validation of coexisting attractors in different basins, several approaches such as bifurcation diagrams, Lyapunov exponents, and the Poincaré section are applied. The second half of the study synchronizes two mechanical chaotic systems using a novel controller, with gyrostat and quadrotor unmanned aerial vehicle (QUAV) chaotic systems acting as master and slave systems, respectively. The error dynamical system and the parameter updated law are built using Lyapunov’s theory, and it is discovered that under certain parametric conditions, the trajectories of the QUAV chaotic system overlap and begin to match the features of the gyrostat chaotic system. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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Article
Mathematical Modeling of the Operation of an Expander-Generator Pressure Regulator in Non-Stationary Conditions of Small Gas Pressure Reduction Stations
Mathematics 2022, 10(3), 393; https://doi.org/10.3390/math10030393 - 27 Jan 2022
Cited by 1 | Viewed by 680
Abstract
Long-distance gas transfer requires high pressure, which has to be reduced before the gas is conveyed to the customers. This pressure reduction takes place at natural gas pressure reduction stations, where gas pressure is decreased by using gas flow energy for overcoming local [...] Read more.
Long-distance gas transfer requires high pressure, which has to be reduced before the gas is conveyed to the customers. This pressure reduction takes place at natural gas pressure reduction stations, where gas pressure is decreased by using gas flow energy for overcoming local resistance, represented by a throttling valve. This pressure energy can be reused, but it is difficult to implement it at small pressure reduction stations, as the values of unsteadiness significantly increase when the gas approaches consumers, whereas gas flow rate and pressure decrease. This work suggests replacing throttling valves at small pressure reduction stations for expander-generator units, based on volumetric expanders. Two implementations are proposed. A mathematical model of gas-dynamic processes, which take place in expander-generator units, was developed using math equations. With its help, a comparison was made of the stability of the operation of two possible control schemes in non-stationary conditions, and the feasibility of using an expander-generator regulator as a primary one for a small natural gas pressure reduction station was confirmed. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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Article
Modelling of Heat Transfer Processes in Heat Exchangers for Cardiopulmonary Bypass
Mathematics 2021, 9(23), 3125; https://doi.org/10.3390/math9233125 - 04 Dec 2021
Viewed by 535
Abstract
A model of the heat exchange process in the heat exchanger of the cardiopulmonary bypass device is proposed which allows for automation of the process of temperature regulation in the cardiopulmonary bypass with an accuracy of ±1 °C during cardiac surgery under controlled [...] Read more.
A model of the heat exchange process in the heat exchanger of the cardiopulmonary bypass device is proposed which allows for automation of the process of temperature regulation in the cardiopulmonary bypass with an accuracy of ±1 °C during cardiac surgery under controlled cooling and warming of the patient’s heart and brain. The purpose of this research is to create a concept and model of the temperature control circuit using the MSC Easy5 system, the creation of mathematical models of blocks of the temperature control circuit, and the description of the principle of temperature control in the cardiopulmonary bypass circuit. The model of the temperature control loop in the heat exchanger of the heart-lung machine was created using the MSC Easy5 system with a programmable microcontroller. The microcontroller implements a specialized temperature control algorithm in the C language. The model allows the creation of a full-fledged virtual prototype of a temperature control device in a heat exchanger, and helps to conduct virtual tests of the developed device at the design stage. The model identifies control system flaws and influences decisions made before producing an official prototype of the product. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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Article
Symmetry Preserving Discretization of the Hamiltonian Systems with Holonomic Constraints
Mathematics 2021, 9(22), 2959; https://doi.org/10.3390/math9222959 - 19 Nov 2021
Viewed by 370
Abstract
Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry [...] Read more.
Symmetry preserving difference schemes approximating equations of Hamiltonian systems are presented in this paper. For holonomic systems in the Hamiltonian framework, the symmetrical operators are obtained by solving the determining equations of Lie symmetry with the Maple procedure. The difference type of symmetry preserving invariants are constructed based on the three points of the lattice and the characteristic equations. The difference scheme is constructed by using these discrete invariants. An example is presented to illustrate the applications of the results. The solutions of the invariant numerical schemes are compared to the noninvariant ones, the standard and the exact solutions. Full article
(This article belongs to the Special Issue Applied Mathematical Modelling and Dynamical Systems)
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