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Dynamical Systems and Their Applications Methods, 2nd Edition
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Dynamical Systems and Their Applications Methods, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: closed (30 September 2024) | Viewed by 3161

Special Issue Editor

Prof. Dr. Marek Lampart

E-Mail Website
Guest Editor
IT4Innovations, Department of Applied Mathematics, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
Interests: dynamical systems; chaos; 0-1 test for chaos; hidden attractor; multistability
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent decades, non-linear phenomena have garnered the attention of researchers across many scientific fields. Simultaneously, the development of technological devices and advanced theories have resulted in new scientific findings in the area of dynamical systems, which in turn have opened novel prospectives in science and engineering fields.

This Special Issue, ‘Dynamical Systems and Their Applications: Second Edition’ invites submissions of original research and survey articles that underscore the recent and novel developments in the theory of dynamical systems and their applications, particularly focusing on analytical, numerical, and experimental results showing non-linear phenomena with regular and irregular patterns.

Prof. Dr. Marek Lampart
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. 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

  • dynamical systems
  • differential and difference equations
  • chaos, chaos control, and anticontrol
  • stability, multi-stability, hidden and self-excited attractors
  • entropy, 0–1 test for chaos, and lyapunov exponent
  • time series, time-series forecasting, and predictability

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Related Special Issue

Published Papers (3 papers)

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Research

19 pages, 11451 KiB  
Article
Truncation Error of the Network Simulation Method: Chaotic Dynamical Systems in Mechanical Engineering
by Joaquín Solano, Javier Mulas-Pérez, Francisco Balibrea and José Andrés Moreno-Nicolás
Mathematics 2024, 12(21), 3441; https://doi.org/10.3390/math12213441 - 4 Nov 2024
Cited by 1 | Viewed by 915
Abstract
This article focuses on the study of local truncation errors (LTEs) in the Network Simulation Method (NSM), specifically when using the trapezoidal method and Gear’s methods. The NSM, which represents differential equations through electrical circuit elements, offers advantages in solving nonlinear dynamic systems [...] Read more.
This article focuses on the study of local truncation errors (LTEs) in the Network Simulation Method (NSM), specifically when using the trapezoidal method and Gear’s methods. The NSM, which represents differential equations through electrical circuit elements, offers advantages in solving nonlinear dynamic systems such as the van der Pol equation. The analysis compares the performance of these numerical methods in terms of their stability and error minimization, with particular emphasis on LTE. By leveraging circuit-based techniques prior to numerical application, the NSM improves convergence. This study evaluates the impact of step size on LTE and highlights the trade-offs between accuracy and computational cost when using the trapezoidal and Gear methods. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods, 2nd Edition)
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20 pages, 3582 KiB  
Article
Preview Control for Cyber–Physical Systems under Periodic Denial-of-Service Attacks
by Jiang Wu, Hao Xie, Jinming Liang and Zhiqiang Li
Mathematics 2024, 12(17), 2653; https://doi.org/10.3390/math12172653 - 27 Aug 2024
Cited by 1 | Viewed by 640
Abstract
In this paper, the preview control problem for cyber–physical systems (CPSs) under denial-of-service (DOS) attacks is studied. First, we employ an attack-tolerant strategy to design an augmented error system (AES) for scenarios where both state and reference signal channels are subject to periodic [...] Read more.
In this paper, the preview control problem for cyber–physical systems (CPSs) under denial-of-service (DOS) attacks is studied. First, we employ an attack-tolerant strategy to design an augmented error system (AES) for scenarios where both state and reference signal channels are subject to periodic attacks. We then discuss the stochastic stability conditions for the AES and derive the corresponding controller. Subsequently, the preview controller for the original system is developed. Finally, the effectiveness of the obtained results is demonstrated through a numerical simulation using an unmanned ground vehicle (UGV) model, indicating the practical applicability of the proposed control strategy. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods, 2nd Edition)
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16 pages, 287 KiB  
Article
Applications of Structural Nabla Derivatives on Time Scales to Dynamic Equations
by Amin Benaissa Cherif, Bouharket Bendouma, Khaled Zennir, Svetlin G. Georgiev, Keltoum Bouhali and Taha Radwan
Mathematics 2024, 12(11), 1688; https://doi.org/10.3390/math12111688 - 29 May 2024
Cited by 1 | Viewed by 1056
Abstract
We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an [...] Read more.
We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an initial value problem characterized by structural Nabla derivatives on timescales. Furthermore, some features of the new operator are proven and illustrated by using concrete examples. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods, 2nd Edition)
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