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Applications of Chaos Theory to Complex Systems Analysis in Engineering

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (19 January 2025) | Viewed by 3373

Special Issue Editors


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Guest Editor
Laboratory of Systems Engineering and Robotics (LASER), Universidade Federal da Paraiba (UFPB), João Pessoa 58051-900, Brazil
Interests: embedded systems; chaos analysis; artificial intelligence; drones; high-performance computing

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Guest Editor
Department of Mechanical Engineering, Universidade Federal da Paraiba (UFPB), João Pessoa 58051-900, Brazil
Interests: mechanical engineering; chaos analysis; signal processing; sound analysis; vibration

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Guest Editor
Department of Physics, Universidade Federal da Paraiba (UFPB), João Pessoa 58051-900, Brazil
Interests: chaos analysis; nuclear physics; mesoscopic fluctuations; graphene; topological insulators

Special Issue Information

Dear Colleagues,

In the field of engineering, the application of chaos theory holds profound importance in understanding and managing complex systems. Chaos theory's significance stems from its ability to unravel the intricate dynamics of nonlinear systems, a common occurrence in real-world engineering problems.

Chaos theory aids engineers in comprehending the complexities of nonlinear behavior, providing a deeper understanding of systems such as fluid dynamics, electrical circuits, and weather patterns. It introduces the concept of deterministic chaos, allowing engineers to predict the seemingly random behaviors in deterministic systems. This predictive power is invaluable in safety-critical applications like aerospace design.

Moreover, chaos theory offers tools for optimizing and controlling complex systems. Engineers can use chaos control techniques to stabilize chaotic systems and enhance overall system performance. This capability has applications in various domains, including robotics, power grids, and chemical processes.

Additionally, chaos theory fosters innovation by encouraging creative problem solving and the exploration of unconventional solutions. It equips engineers with the tools to design more resilient systems by analyzing responses to disturbances and external factors.

This Special Issue focuses on publishing new and improved techniques to analyze low-dimensional chaotic dynamics, as well as complex interacting systems (e.g., flocks and networks), mainly presenting how chaos theory empowers engineers to navigate challenges, predict and manage unpredictability, optimize performance, drive innovation, and build robust and resilient systems. The authors are encouraged (but not limited) to discuss entropy-related aspects of chaos theory, for example, entropy and information theory, sensitivity to initial conditions, entropy as a measure of uncertainty, chaos in statistical mechanics, and quantification of chaos and entropy. Common applications of entropy and chaos theory in engineering are as follows:

  • Dynamical system analysis;
  • Vibrational analysis;
  • Fluid dynamics;
  • Control systems;
  • Communication systems;
  • Environmental engineering;
  • Electronic circuits;
  • Secure communication and cryptography;
  • Energy and power systems;
  • Aeronautics and space exploration;
  • Biomedical engineering;
  • Materials science;
  • Quality control.

Prof. Dr. Alisson Brito
Prof. Dr. Abel Cavalcante Lima Filho
Prof. Dr. Jorge Gabriel G. S. Ramos
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. Entropy 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 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

  • nonlinearity
  • complex systems
  • detection and diagnosis of failure
  • deterministic chaos
  • predictability
  • optimization
  • control
  • robustness
  • resilience
  • fault tolerance

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Published Papers (2 papers)

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Research

24 pages, 1324 KiB  
Article
The Nonlinear Dynamics and Chaos Control of Pricing Games in Group Robot Systems
by Chen Wang, Yi Sun, Ying Han and Chao Zhang
Entropy 2025, 27(2), 164; https://doi.org/10.3390/e27020164 - 4 Feb 2025
Viewed by 753
Abstract
System stability control in resource allocation is a critical issue in group robot systems. Against this backdrop, this study investigates the nonlinear dynamics and chaotic phenomena that arise during pricing games among finitely rational group robots and proposes control strategies to mitigate chaotic [...] Read more.
System stability control in resource allocation is a critical issue in group robot systems. Against this backdrop, this study investigates the nonlinear dynamics and chaotic phenomena that arise during pricing games among finitely rational group robots and proposes control strategies to mitigate chaotic behaviors. A system model and a business model for group robots are developed based on market mechanism mapping, and the dynamics of resource allocation are formulated as a second-order discrete nonlinear system using game theory. Numerical simulations reveal that small perturbations in system parameters, such as pricing adjustment speed, product demand coefficients, and resource substitution coefficients, can induce chaotic behaviors. To address these chaotic phenomena, a control method combining state feedback and parameter adjustment is proposed. This approach dynamically tunes the state feedback intensity of the system via a control parameter M, thereby delaying bifurcations and suppressing chaotic behaviors. It ensures that the distribution of system eigenvalues satisfies stability conditions, allowing control over unstable periodic orbits and period-doubling bifurcations. Simulation results demonstrate that the proposed control method effectively delays period-doubling bifurcations and stabilizes unstable periodic orbits in chaotic attractors. The stability of the system’s Nash equilibrium is significantly improved, and the parameter range for equilibrium pricing is expanded. These findings provide essential theoretical foundations and practical guidance for the design and application of group robot systems. Full article
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22 pages, 5006 KiB  
Article
Sensorless Speed Estimation of Induction Motors through Signal Analysis Based on Chaos Using Density of Maxima
by Marlio Antonio Silva, Jose Anselmo Lucena-Junior, Julio Cesar da Silva, Francisco Antonio Belo, Abel Cavalcante Lima-Filho, Jorge Gabriel Gomes de Souza Ramos, Romulo Camara and Alisson Brito
Entropy 2024, 26(5), 361; https://doi.org/10.3390/e26050361 - 25 Apr 2024
Cited by 2 | Viewed by 1817
Abstract
Three-phase induction motors are widely used in various industrial sectors and are responsible for a significant portion of the total electrical energy consumed. To ensure their efficient operation, it is necessary to apply control systems with specific algorithms able to estimate rotation speed [...] Read more.
Three-phase induction motors are widely used in various industrial sectors and are responsible for a significant portion of the total electrical energy consumed. To ensure their efficient operation, it is necessary to apply control systems with specific algorithms able to estimate rotation speed accurately and with an adequate response time. However, the angular speed sensors used in induction motors are generally expensive and unreliable, and they may be unsuitable for use in hostile environments. This paper presents an algorithm for speed estimation in three-phase induction motors using the chaotic variable of maximum density. The technique used in this work analyzes the current signals from the motor power supply without invasive sensors on its structure. The results show that speed estimation is achieved with a response time lower than that obtained by classical techniques based on the Fourier Transform. This technique allows for the provision of motor shaft speed values when operated under variable load. Full article
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