Artificial Neural Networks: Alpha Unpredictability and Chaotic Dynamics (人工神經網絡：阿爾法不可預測性與混沌動態)

Akhmet, Marat, Tleubergenova, Madina, Zhamanshin, Akylbek

Artificial Neural Networks: Alpha Unpredictability and Chaotic Dynamics
  • 出版商: Springer
  • 出版日期: 2024-10-23
  • 售價: $6,540
  • 貴賓價: 9.5 折 $6,213
  • 語言: 英文
  • 頁數: 251
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031689658
  • ISBN-13: 9783031689659

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商品描述

Mathematical chaos in neural networks is a powerful tool that reflects the world's complexity and has the potential to uncover the mysteries of the brain's intellectual activity. Through this monograph, the authors aim to contribute to modern chaos research, combining it with the fundamentals of classical dynamical systems and differential equations. The readers should be reassured that an in-depth understanding of chaos theory is not a prerequisite for working in the area designed by the authors. Those interested in the discussion can have a basic understanding of ordinary differential equations and the existence of bounded solutions of quasi-linear systems on the real axis.

Based on the novelties, this monograph aims to provide one of the most powerful approaches to studying complexities in neural networks through mathematical methods in differential equations and, consequently, to create circumstances for a deep comprehension of brain activity and artificial intelligence. A large part of the book consists of newly obtained contributions to the theory of recurrent functions, Poisson stable, and alpha unpredictable solutions and ultra Poincaré chaos of quasi-linear and strongly nonlinear neural networks such as Hopfield neural networks, shunting inhibitory cellular neural networks, inertial neural networks, and Cohen-Grossberg neural networks.

The methods and results presented in this book are meant to benefit senior researchers, engineers, and specialists working in artificial neural networks, machine and deep learning, computer science, quantum computers, and applied and pure mathematics. This broad applicability underscores the value and relevance of this research area to a large academic community and the potential impact it can have on various fields.

商品描述(中文翻譯)

數學混沌在神經網絡中是一種強大的工具，反映了世界的複雜性，並有潛力揭示大腦智力活動的奧秘。通過這本專著，作者旨在為現代混沌研究做出貢獻，將其與經典動力系統和微分方程的基本原理相結合。讀者應該放心，對混沌理論的深入理解並不是從事作者所設計領域的先決條件。對於有興趣參與討論的人來說，對常微分方程的基本理解以及對實數軸上準線性系統有界解的存在有一定認識即可。

基於這些新穎性，本專著旨在通過微分方程中的數學方法提供研究神經網絡複雜性的一種最強大方法，並因此創造出深入理解大腦活動和人工智慧的條件。本書的大部分內容包括對遞歸函數、泊松穩定解、α不可預測解以及準線性和強非線性神經網絡（如霍普菲爾德神經網絡、分流抑制細胞神經網絡、慣性神經網絡和科恩-格羅斯伯格神經網絡）的超級龐加萊混沌理論的新貢獻。

本書中所呈現的方法和結果旨在惠及從事人工神經網絡、機器學習和深度學習、計算機科學、量子計算以及應用數學和純數學的高級研究人員、工程師和專家。這種廣泛的適用性突顯了這一研究領域對於大型學術社群的價值和相關性，以及它對各個領域可能產生的影響。

作者簡介

Marat Akhmet is currently a Professor of Mathematics at Middle East Technical University in Ankara, Türkiye. He received his bachelor's degree in Mathematics from Aktobe State University in Kazakhstan and his Doctorate in Differential Equations and Mathematical Physics from Kyiv State University in Ukraine. M. Akhmet has been awarded the Science Prize of TUBITAK (Türkiye, 2015) for his achievements in scientific research and the Prof C.S. Hsu Award (UC Berkeley, 2021) for outstanding results in non-linear analysis investigations. Has been invited as a Plenary speaker for 17 international conferences in the UK, Kazakhstan, Türkiye, the USA, France, and Italy, and organized more than 20 international and national scientific meetings. Dr. Akhmet is passionate about scientific research and his role as a teacher, and he has continuously been one of the recipients of the "Best Performance Award" at Middle East Technical University over the 20 years of his work there. Dr. Akhmet has mentored 20 Ph.D. students over his career, who now work in research centers and universities in Türkiye, Kazakhstan, and Libya. Dr. Marat Akhmet's research focuses on dynamical models and differential equations. He has published seven Springer books and more than 150 scientific papers. In the last several years, he has been investigating the dynamics of neural networks, almost periodic motions, stability, synchronization, chaos, and fractals.

Madina Tleubergenova is an Associate professor of Mathematics, working as the head of the Mathematics department at K. Zhubanov Aktobe Regional University. She received her Bachelor's degree in Mathematics at K. Zhubanov Aktobe State University and her Doctoral degree in Physical and Mathematical Sciences at Al-Farabi Kazakh National University, Kazakhstan. She is the head of research on fundamental research projects of the Ministry of Higher Education and Science of the Republic of Kazakhstan, and the winner of the "Best University Teacher 2020" prize awarded by the Republic of Kazakhstan.

Akylbek Zhamanshin is an Associate professor of Mathematics at the Herriot-Watt International Faculty of Aktobe Regional University, Aktobe, Kazakhstan. He received his PhD degree in Mathematics at Aktobe Regional University and was a postdoctoral researcher at Middle East Technical University, Ankara, Türkiye. His research interests include differential equations, dynamical systems, complex dynamics, neural networks, and chaos.

Zakhira Nugayeva is a Mathematics teacher at the Department of Mathematics of Aktobe Regional University, Aktobe, Kazakhstan. She received her PhD degree in Mathematics at Aktobe Regional University. Her research interests include differential equations, impulsive systems, complex dynamics, neural networks, and chaos. She won the title "Best University Teacher 2023" in Kazakhstan.

作者簡介(中文翻譯)

**Marat Akhmet** 目前是土耳其安卡拉中東科技大學的數學教授。他在哈薩克斯坦的阿克托貝國立大學獲得數學學士學位，並在烏克蘭基輔國立大學獲得微分方程和數學物理的博士學位。M. Akhmet因其在科學研究方面的成就而獲得了土耳其科學技術研究委員會（TUBITAK）於2015年頒發的科學獎，以及加州大學伯克利分校於2021年頒發的C.S. Hsu教授獎，以表彰他在非線性分析研究中的卓越成果。他曾受邀擔任英國、哈薩克斯坦、土耳其、美國、法國和意大利17場國際會議的全體演講者，並組織了20多場國際和國內的科學會議。Akhmet博士對科學研究和教學充滿熱情，在中東科技大學工作20年以來，他持續獲得「最佳表現獎」。Akhmet博士在其職業生涯中指導了20名博士生，這些學生目前在土耳其、哈薩克斯坦和利比亞的研究中心和大學工作。Marat Akhmet博士的研究重點是動態模型和微分方程。他已出版七本Springer書籍和超過150篇科學論文。在過去幾年中，他一直在研究神經網絡的動態、幾乎周期運動、穩定性、同步、混沌和分形。

**Madina Tleubergenova** 是哈薩克斯坦K. Zhubanov阿克托貝區域大學的數學副教授，並擔任數學系主任。她在K. Zhubanov阿克托貝國立大學獲得數學學士學位，並在哈薩克阿法拉比國立大學獲得物理和數學科學的博士學位。她是哈薩克斯坦共和國高等教育和科學部基礎研究項目的研究負責人，並獲得了哈薩克斯坦共和國頒發的「2020年最佳大學教師」獎。

**Akylbek Zhamanshin** 是哈薩克斯坦阿克托貝區域大學赫里奧特-瓦特國際學院的數學副教授。他在阿克托貝區域大學獲得數學博士學位，並曾在土耳其安卡拉的中東科技大學擔任博士後研究員。他的研究興趣包括微分方程、動態系統、複雜動力學、神經網絡和混沌。

**Zakhira Nugayeva** 是哈薩克斯坦阿克托貝區域大學數學系的數學教師。她在阿克托貝區域大學獲得數學博士學位。她的研究興趣包括微分方程、脈衝系統、複雜動力學、神經網絡和混沌。她在哈薩克斯坦獲得了「2023年最佳大學教師」的稱號。

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