Application of Mathematical Method and Models in Dynamic System, 3rd Edition

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 20 January 2027 | Viewed by 760

Editor


E-Mail Website
Guest Editor
Department of Mathematics, Politehnica University of Timişoara, Piata Victoriei No. 2, 300006 Timisoara, Romania
Interests: Hamilton-Poisson systems; nonlinear dynamical systems; bifurcations; mathematical models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The most observed phenomena in scientific investigation and in everyday life are dynamic phenomena. The list of these phenomena is extensive, including life systems, physical systems, and social systems, which encompass population growth, ecological decay, epidemics of disease, the motion of a system of particles, the behavior of an economic structure, etc. Some of these phenomena are easy to understand, but others require a proper mathematical model, which is usually represented in terms of either differential or difference equations. This includes continuous-time dynamical systems, piecewise dynamical systems, discrete-time dynamical systems, time-delay dynamical systems, fractional order dynamical systems, and fast–slow dynamical systems, among others.

The aim of this Special Issue is to establish new mathematical models and study their behavior and properties, and to study those of existing dynamical systems by using known or new methods.

Dr. Cristian Lazureanu
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 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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

  • mathematical models
  • dynamic systems
  • bifurcations
  • chaotic behavior
  • controllability
  • integrability
  • numerical methods
  • numerical simulations
  • stability

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (2 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

34 pages, 924 KB  
Article
Multistage Optimal Parametric Iteration Method Applied to Generate Closed-Form Solutions for Dynamical System with Quadratic Nonlinearities
by Remus-Daniel Ene, Romeo Negrea, Rodica Badarau and Nicolina Pop
Mathematics 2026, 14(17), 3165; https://doi.org/10.3390/math14173165 - 2 Sep 2026
Viewed by 175
Abstract
This paper investigates the damped and periodical oscillations of a specific system that depends on four physical parameters. Exact parametric solutions are established based on a smooth function. The system is explicitly integrated without admitting prime integrals. The influence of the physical parameters [...] Read more.
This paper investigates the damped and periodical oscillations of a specific system that depends on four physical parameters. Exact parametric solutions are established based on a smooth function. The system is explicitly integrated without admitting prime integrals. The influence of the physical parameters is examined semi-analytically through the Multistage Optimal Parametric Iteration Method (MOPIM). A key advantage of this method is that it used only one iteration, owing to an appropriate choice of auxiliary functions for convergence control. There is accuracy between MOPIM solutions and corresponding numerical results, highlighted qualitatively through figures, quantitatively through tables, and by statistical tests of the residuals. The damped or periodical behaviors of the system’s solutions lead to their application on electronic circuits or other technological application fields. Full article
Show Figures

Figure 1

29 pages, 6474 KB  
Article
Performance Comparison of 15-Phase and 9-Phase Permanent Magnet Synchronous Generators Under Healthy, Fault, and Fault-Tolerant Control Conditions: A VSD-Based Analysis
by Ahad Fatahi, Mohamed Fouad Benkhoris, Djamel Ziane and Mohamed Assaad Hamida
Mathematics 2026, 14(17), 3148; https://doi.org/10.3390/math14173148 - 1 Sep 2026
Viewed by 251
Abstract
Multi-phase permanent magnet synchronous generators (PMSGs) are increasingly adopted in renewable energy systems and isolated microgrids due to their improved fault tolerance, reduced per-phase current stress, and enhanced power density compared to conventional three-phase machines. This article presents a systematic performance comparison between [...] Read more.
Multi-phase permanent magnet synchronous generators (PMSGs) are increasingly adopted in renewable energy systems and isolated microgrids due to their improved fault tolerance, reduced per-phase current stress, and enhanced power density compared to conventional three-phase machines. This article presents a systematic performance comparison between 15-phase and 9-phase PMSGs under four distinct operating conditions: healthy mode, single-phase open-circuit fault (Phase 1), and two fault-tolerant control (FTC) strategies. The first FTC technique involves opening a second phase with approximately 90-degree phase displacement from the faulty phase to attenuate power oscillations and reduce current amplitude imbalances. The second technique involves isolating a complete three-phase set containing the faulty phase without adapting the machine model. Both machines are modeled using the vector space decomposition (VSD) approach under field-oriented control (FOC), and simulations are performed in MATLAB/Simulink. Performance metrics include power efficiency, power losses, power ripple factor, electromagnetic power ripple, stator RMS current evolution, and stator current balance. Results demonstrate that the 15-phase PMSG consistently exhibits lower power ripple (6.5% vs. 15.54% under open-circuit fault), higher efficiency (89.02% vs. 87.44%), and reduced power losses across all fault scenarios. The first fault-tolerant strategy improves performance in both machines but is more effective in the 15-phase configuration. To validate the findings beyond offline simulation, hardware-in-the-loop (HIL) experiments are conducted on an OPAL-RT real-time platform, where the complete system—the PMSG and converter models together with the FOC and fault-tolerant control algorithms—is implemented within its FPGA framework. The HIL results for electromagnetic power and d–q axis stator currents show close agreement with the MATLAB/Simulink results across all operating conditions, confirming the FPGA implementability of the proposed control strategies under real-time constraints. These findings provide actionable insights for the design and control of high-phase-count generators in grid-connected and isolated power systems. Full article
Show Figures

Figure 1

Back to TopTop