Optimization Of Integer Fractional Order Chaotic Systems By Metaheuristics And Their Electronic Realization
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Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization
Mathematicians have devised different chaotic systems that are modeled by integer or fractional-order differential equations, and whose mathematical models can generate chaos or hyperchaos. The numerical methods to simulate those integer and fractional-order chaotic systems are quite different and their exactness is responsible in the evaluation of characteristics like Lyapunov exponents, Kaplan-Yorke dimension, and entropy. One challenge is estimating the step-size to run a numerical method. It can be done analyzing the eigenvalues of self-excited attractors, while for hidden attractors it is difficult to evaluate the equilibrium points that are required to formulate the Jacobian matrices. Time simulation of fractional-order chaotic oscillators also requires estimating a memory length to achieve exact results, and it is associated to memories in hardware design. In this manner, simulating chaotic/hyperchaotic oscillators of integer/fractional-order and with self-excited/hidden attractors is quite important to evaluate their Lyapunov exponents, Kaplan-Yorke dimension and entropy. Further, to improve the dynamics of the oscillators, their main characteristics can be optimized applying metaheuristics, which basically consists of varying the values of the coefficients of a mathematical model. The optimized models can then be implemented using commercially available amplifiers, field-programmable analog arrays (FPAA), field-programmable gate arrays (FPGA), microcontrollers, graphic processing units, and even using nanometer technology of integrated circuits. The book describes the application of different numerical methods to simulate integer/fractional-order chaotic systems. These methods are used within optimization loops to maximize positive Lyapunov exponents, Kaplan-Yorke dimension, and entropy. Single and multi-objective optimization approaches applying metaheuristics are described, as well as their tuning techniques to generate feasible solutions that are suitable for electronic implementation. The book details several applications of chaotic oscillators such as in random bit/number generators, cryptography, secure communications, robotics, and Internet of Things.
Complex Systems and Their Applications
Author: Guillermo Huerta Cuéllar
language: en
Publisher: Springer Nature
Release Date: 2022-06-10
This book is a compilation of scientific articles written by recognized researchers, and select students, participating in the Second Conference on the Study of Complex Systems and their Applications (EDIESCA 2021). EDIESCA 2021 arose from the need for academic and research groups that carry out this scientific research to disseminate their results internationally. The study and characterization of systems with non-linear and/or chaotic behavior has been of great interest to researchers around the world, for which many important results have been obtained with various applications. The dynamic study of chaotic oscillators of different models, such as Rössler, Lorenz, and Chua, has generated important advances in understanding of chemical reactions, meteorological behavior, design of electronic devices, and other applications. Topics at the event included applications for communications systems by masking techniques, financial behavior, networks analysis, nonlinear lasers, numerical modeling, electronic design, and other interesting topics in the area of complex systems. Additionally, there are results on numerical simulation and electronic designs to generate complex dynamic behaviors.
Random Number Generators
Author: Luis Gerardo de la Fraga
language: en
Publisher: Springer Nature
Release Date: 2025-05-17
This book discusses the details of random number generation (RNG) as a key technology that is used for information security in various fields, such as electronic commerce and authentication. Readers will see how random numbers are used in various applications such as in the generation of keys for data encryption, games, lotteries, sampling, simulations, statistical sampling, search/sort algorithms, and gambling. The authors describe how the classification of RNGs encompasses linear and nonlinear (chaotic) pseudo and truly random number generators, and how they can be evaluated by applying statistical tests. Covers a vast array of special topics on fractional-order chaotic circuits and systems to develop applications in information security; Describes details of using FPGAs to approach chaotic maps and fractional-order circuits and systems for hardware security; Includes Verilog hardware description for random number generation.