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 "Engineering Mathematics".

Deadline for manuscript submissions: 31 August 2024 | Viewed by 3777

Special Issue Editor


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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
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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

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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

Published Papers (2 papers)

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Research

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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 838
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
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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 - 04 Nov 2022
Cited by 9 | Viewed by 2481
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
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