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Mathematical Modeling, Analysis, and Applications of Complex Dynamics in Electrical...
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Mathematical Modeling, Analysis, and Applications of Complex Dynamics in Electrical Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 8045

Special Issue Editor

Dr. Jiri Petrzela

E-Mail Website
Guest Editor
Department of Radio Electronics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic
Interests: analog circuits; nonlinear dynamics; chaos theory; oscillators; frequency filters
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Analog, digital, and mixed-mode networks can be modeled using suitable mathematical tools, such as set of ordinary and partial differential equations, algebraic expressions, and logic functions. Mathematical models are usually constructed to be as simple as possible, with respect to intended function of investigated electronic system. However, in such a case, many important features of modeled electronic systems can be neglected, and we can experience significant differences between measured and simulated results.

During the last few decades of intensive research, many building blocks dedicated to signal generation and processing have exhibit a complex behavior whose character is different from that of conventional, i.e., expected function. New numerical methods along with high-performance computers allow us to analyze mathematical models with increased complexity, considering many degrees of freedom, having elements working in different time scales or mathematical models with strongly nonlinear components, etc.

This Special Issue welcomes all contributions focused on the complex dynamical behavior of electronic circuits, introducing novel nonlinear systems having some unique properties, including the design of chaotic or hyperchaotic systems and its application in communication techniques. It also includes papers describing applications of new numerical algorithms on various electronic networks, research and review works on the mathematical methods developed for specific engineering problems, or the successful use of known mathematical approaches to answer important questions from the area of general electronics.

Dr. Jiri Petrzela
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

  • analog and digital networks
  • applications of chaos in electronics
  • complex behavior
  • computer-aided analysis of circuits
  • deterministic dynamical system
  • fractal dimension
  • chaos and hyperchaos
  • mathematical modeling
  • nonlinear dynamics
  • signal processing
  • strange attractors

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Published Papers (3 papers)

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Research

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17 pages, 1182 KiB  
Article
Synchronization of Chaotic Systems with Huygens-like Coupling
by Jonatan Pena Ramirez, Adrian Arellano-Delgado, Rodrigo Méndez-Ramírez and Hector Javier Estrada-Garcia
Mathematics 2024, 12(20), 3177; https://doi.org/10.3390/math12203177 - 11 Oct 2024
Cited by 1 | Viewed by 1185
Abstract
One of the earliest reports on synchronization of inert systems dates back to the time of the Dutch scientist Christiaan Huygens, who discovered that a pair of pendulum clocks coupled through a wooden bar oscillate in harmony. A remarkable feature in Huygens’ experiment [...] Read more.
One of the earliest reports on synchronization of inert systems dates back to the time of the Dutch scientist Christiaan Huygens, who discovered that a pair of pendulum clocks coupled through a wooden bar oscillate in harmony. A remarkable feature in Huygens’ experiment is that different synchronous behaviors may be observed by just changing a parameter in the coupling. Motivated by this, in this paper, we propose a novel synchronization scheme for chaotic oscillators, in which the design of the coupling is inspired in Huygens’ experiment. It is demonstrated that the coupled oscillators may exhibit not only complete synchronization, but also mixed synchronization—some states synchronize in anti-phase whereas other states synchronize in-phase—depending on a single parameter of the coupling. Additionally, the stability of the synchronous solution is investigated by using the master stability function approach and the largest transverse Lyapunov exponent. The Lorenz system is considered as particular application example, and the performance of the proposed synchronization scheme is illustrated with computer simulations and validated by means of experiments using electronic circuits. Full article
(This article belongs to the Special Issue Mathematical Modeling, Analysis, and Applications of Complex Dynamics in Electrical Engineering)
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18 pages, 5701 KiB  
Article
Mathematical Expressions Useful for Tunable Properties of Simple Square Wave Generators
by Roman Sotner and Jan Jerabek
Mathematics 2022, 10(23), 4528; https://doi.org/10.3390/math10234528 - 30 Nov 2022
Viewed by 1352
Abstract
This paper compares two electronically controllable solutions of triangular and square wave generators benefiting from a single IC package including all necessary active elements (modular cells fabricated in I3T 0.35 µm ON Semiconductor process operating with ±1.65 V supply voltage). Internal cells are [...] Read more.
This paper compares two electronically controllable solutions of triangular and square wave generators benefiting from a single IC package including all necessary active elements (modular cells fabricated in I3T 0.35 µm ON Semiconductor process operating with ±1.65 V supply voltage). Internal cells are used for construction of building blocks of the generator (integrator and Schmitt trigger/comparator). Proposed solutions have adjustable parameters dependent on the values of DC control voltages and currents. Attention is given to the mathematical expressions for the advantageous tunability of these generators. Theoretical mathematical functions comparing the standard linear formula with special expression for the frequency adjustment are evaluated and compared with experimentally obtained results. Mathematical functions prove that the proposed topologies improve efficiency of tunability and reduce overall complexity of both generators. Features of proposed solutions were verified experimentally. Both single-parameter tunable designs target on the operation in bands from tens to hundreds of kHz (from 13 kHz up to 251 kHz for the driving voltage between 0.05 V and 1.0 V for the first solution; from 12 kHz up to 847 kHz for the driving current between 5 µA and 140 µA for the second solution). A comparison with similar solutions indicates beneficial performance of the proposed solutions in tunability ratio vs. driving parameter ratio and also because simplicity of circuitry is low. The qualitative evaluation and comparison of parameters of both circuits is given and confirms theoretical expectations. Full article
(This article belongs to the Special Issue Mathematical Modeling, Analysis, and Applications of Complex Dynamics in Electrical Engineering)
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Review

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28 pages, 9602 KiB  
Review
Chaos in Analog Electronic Circuits: Comprehensive Review, Solved Problems, Open Topics and Small Example
by Jiri Petrzela
Mathematics 2022, 10(21), 4108; https://doi.org/10.3390/math10214108 - 4 Nov 2022
Cited by 16 | Viewed by 4724
Abstract
This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries [...] Read more.
This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements. Full article
(This article belongs to the Special Issue Mathematical Modeling, Analysis, and Applications of Complex Dynamics in Electrical Engineering)
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