Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization
暫譯: 元啟發式優化整數/分數階混沌系統及其電子實現

Tlelo-Cuautle, Esteban, Gerardo de la Fraga, Luis, Guillén-Fernández, Omar Guillén

Optimization of Integer/Fractional Order Chaotic Systems by Metaheuristics and their Electronic Realization
  • 出版商: CRC
  • 出版日期: 2021-05-10
  • 售價: $6,450
  • 貴賓價: 9.5 折 $6,128
  • 語言: 英文
  • 頁數: 256
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0367486687
  • ISBN-13: 9780367486686

    • 海外代購書籍(需單獨結帳)

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商品描述

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.

商品描述(中文翻譯)

數學家們設計了不同的混沌系統，這些系統由整數或分數階微分方程建模，其數學模型可以產生混沌或超混沌。模擬這些整數和分數階混沌系統的數值方法相當不同，其精確性對於評估如 Lyapunov 指數、Kaplan-Yorke 維度和熵等特徵至關重要。一個挑戰是估計運行數值方法的步長。這可以通過分析自激吸引子的特徵值來完成，而對於隱藏吸引子，評估所需的平衡點以形成雅可比矩陣則相對困難。分數階混沌振盪器的時間模擬也需要估計記憶長度以達到精確結果，這與硬體設計中的記憶體有關。因此，模擬整數/分數階的混沌/超混沌振盪器以及自激/隱藏吸引子對於評估其 Lyapunov 指數、Kaplan-Yorke 維度和熵是相當重要的。此外，為了改善振盪器的動態特性，可以通過應用元啟發式方法來優化其主要特徵，這基本上是通過改變數學模型的係數值來實現的。優化後的模型可以使用商業可用的放大器、現場可編程類比陣列 (FPAA)、現場可編程閘陣列 (FPGA)、微控制器、圖形處理單元，甚至使用納米技術的集成電路來實現。

本書描述了不同數值方法在模擬整數/分數階混沌系統中的應用。這些方法在優化迴圈中使用，以最大化正的 Lyapunov 指數、Kaplan-Yorke 維度和熵。書中描述了應用元啟發式的單目標和多目標優化方法，以及其調整技術，以生成適合電子實現的可行解。書中詳細介紹了混沌振盪器的幾個應用，例如隨機位元/數字生成器、密碼學、安全通信、機器人技術和物聯網。

作者簡介

Esteban Tlelo-Cuautle is a principal investigator at Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), México. He has authored 4 and edited 11 books, and has published around 300 articles in books, reputed journals and conferences. He is an Associate Editor in IEEE Transactions on Circuits and Systems, Engineering Applications of Artificial Intelligence, MDPI Electronics, Integration the VLSI Journal, and Frontiers of Information Technology and Electronics Engineering. His research interests include analog signal processing, synthesis and design of integrated circuits, optimization by metaheuristics, design and applications of chaotic systems, IoT security, symbolic analysis and analog/RF and mixed-signal design automation tools.

Dr. Luis Gerardo de la Fraga is in the Computer Science Department at the Center of Research and Advanced Studies (Cinvestav), in Mexico City. His research areas include computer vision, application of evolutionary algorithms, applied mathematics, and network security. He is very enthusiastic on open software and GNU/Linux systems. Dr. de la Fraga has published more than 30 articles in reputed journals, 6 in books, 1 book and more than 50 articles in international conferences. He had graduated 27 MSc and 3 PhD students. He is member of the Mexican Academy of Sciences, and Senior Member of the IEEE society. He is also member of ACM society.

Omar Guillén-Fernández received a B.Eng. degree from Instituto Tecnológico de Veracruz, and the M.Sc. degree in Electronics in 2018 from Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE) in México. He is currently pursuing a Ph.D. at INAOE. He has authored 1 book, and around 10 works published in book chapters, international journals and conferences. His topics of interest are oriented to chaotic systems, synchronization techniques, security of data transmission, embedded systems and integrated circuit design and applications.

Alejandro Silva-Juárez received his Engineering degree on Electronics and his M.Sc. degree from Instituto Tecnológico de Puebla, México in 2013. He received a Ph.D. degree from Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), México in 2020. He has authored 1 book, and around 10 works published in book chapters, international journals and conferences. His research interests include modeling, embedded systems, simulation and optimization of chaotic systems, synthesis of analog circuits and fractional-order chaotic systems and applications.

作者簡介(中文翻譯)

Esteban Tlelo-Cuautle 是墨西哥國家天文學、光學與電子學研究所 (INAOE) 的首席研究員。他已撰寫 4 本書並編輯 11 本書，並在書籍、知名期刊和會議上發表了約 300 篇文章。他是《IEEE 電路與系統學報》、《人工智慧工程應用》、《MDPI 電子學》、《VLSI 整合期刊》和《資訊科技與電子工程前沿》的副編輯。他的研究興趣包括類比信號處理、集成電路的合成與設計、元啟發式優化、混沌系統的設計與應用、物聯網安全、符號分析以及類比/RF 和混合信號設計自動化工具。

路易斯·赫拉多·德拉·弗拉加博士在墨西哥城的高級研究中心 (Cinvestav) 計算機科學系工作。他的研究領域包括計算機視覺、進化算法的應用、應用數學和網絡安全。他對開源軟體和 GNU/Linux 系統非常熱衷。德拉·弗拉加博士已在知名期刊上發表了超過 30 篇文章，6 篇書籍，1 本書以及超過 50 篇國際會議文章。他已指導 27 名碩士生和 3 名博士生。他是墨西哥科學院的成員，也是 IEEE 會的高級會員。他同時也是 ACM 會的成員。

奧馬爾·吉連-費爾南德斯在墨西哥韋拉克魯斯技術學院獲得工程學士學位，並於 2018 年在墨西哥國家天文學、光學與電子學研究所 (INAOE) 獲得電子學碩士學位。他目前正在 INAOE 追求博士學位。他已撰寫 1 本書，並在書籍章節、國際期刊和會議上發表了約 10 篇作品。他的研究主題包括混沌系統、同步技術、數據傳輸安全、嵌入式系統以及集成電路的設計與應用。

亞歷杭德羅·西爾瓦-華雷斯於 2013 年在墨西哥普埃布拉技術學院獲得電子工程學位及碩士學位。他於 2020 年在墨西哥國家天文學、光學與電子學研究所 (INAOE) 獲得博士學位。他已撰寫 1 本書，並在書籍章節、國際期刊和會議上發表了約 10 篇作品。他的研究興趣包括建模、嵌入式系統、混沌系統的模擬與優化、類比電路的合成以及分數階混沌系統及其應用。

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