Mathematical Modelling of Complex Patterns Through Fractals and Dynamical Systems (透過分形與動態系統的複雜模式數學建模)

本書提供了超越動態系統、複雜系統和分形幾何領域的多種有趣關聯。通過使用分形方法探索複雜系統及其特性，本書為尚未驗證其專業知識的新領域提供了初步解決方案。此外，本書專注於最新的科學興趣，並在計算機科學、電子工程、電氣工程、生物工程、生物醫學、量子物理和流體動力學研究等多學科領域中闡述一般的分形理論。本書是為數學、計算機科學和物理領域的專業人士設計的，甚至也適合非專業人士，以幫助理解非線性動態系統和複雜系統中的分形概念，同時為純科學和應用科學及工程領域的研究人員提供應用。

A. Gowrisankar received his Ph.D degree (in Mathematics) from the Gandhigram Rural Institute (Deemed to be University), Gandhigram, Dindigul, India, in 2017. He was employed as an institution postdoctoral fellow at the Indian institution of Technology Guwahati (IITG), in Guwahati, Assam, India. He is currently employed as an Assistant Professor in the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India with six years of experience. His broad areas of research include Fractal Analysis, Fractal Interpolation Functions, Fractional Calculus, Nonlinear Dynamics and Climate Change. He has contributed to more than 40 research articles published in reputable international journals. He was successful in getting three books published by the following publishers: CRC Press, 2019, Springer: Complexity, 2021 and SpingerBriefs in Complexity, 2024. He was one of the editors for two edited books in CRC Press and Taylor & Francis Group. He served as a guest editor for two special issues in "The European Physical Journal Special Topics". He is acting as a reviewer for more than 10 international journals and has received the title of "Distinguished EPJ Referees -2021". Recently, he has received a TARE fellowship under SERB, Govt. of India, for the period 2024 - 2026.

Kishore Bingi received the B.Tech. Degree in Electrical and Electronics Engineering from Acharya

Nagarjuna University, India, in 2012. He received the M.Tech. Degree in Instrumentation and Control

Systems from the National Institute of Technology Calicut, India, in 2014, and a PhD in Electrical and

Electronic Engineering from Universiti Teknologi PETRONAS, Malaysia, in 2019. From 2014 to 2015, he

worked as an Assistant Systems Engineer at TATA Consultancy Services Limited, India. From 2019 to 2020, he worked as Research Scientist and Post-Doctoral Researcher at the Universiti Teknologi PETRONAS, Malaysia. From 2020 to 2022, he served as an Assistant Professor at the Process Control Laboratory, School of Electrical Engineering, Vellore Institute of Technology, India. Since 2022 he has been working as a faculty member at the Department of Electrical and Electronic Engineering at Universiti Teknologi PETRONAS, Malaysia. His research area is developing fractional-order neural networks, including fractional-order systems and controllers, chaos prediction and forecasting, and advanced hybrid optimization techniques. He is an IEEE and IET Member and a registered Chartered Engineer (CEng) from Engineering Council UK. He serves as an Editorial Board Member for the International Journal of Applied Mathematics and Computer Science and Academic Editor for Mathematical Problems in Engineering and the Journal of Control Science and Engineering.

Cristina Serpa has a degree in Applied Mathematics - Fundamental Applications, a Master's and a PhD in

Mathematics, in Mathematical Analysis, from the Faculty of Sciences of the University of Lisbon. She is an invited professor in the Mathematics Department of the Instituto Superior de Engenharia de Lisboa of the Instituto Politécnico de Lisboa.Her teaching duties are usually focused on calculus curricular units for engineering. She is an integrated member of CMAFcIO - Center for Mathematics, Fundamental Applications and Operational Research, of the University of Lisbon and collaborates with the Portuguese Mathematical Society. He researches Fractals at the fundamental theoretical level and in the context of their applications. He created the Fractal Regression method, developing corresponding software to obtain fractal functions from real data.

A. Gowrisankar於2017年獲得印度丁迪古爾甘地村大學（被認定為大學）的數學博士學位。他曾在印度阿薩姆邦的印度理工學院古瓦哈提（IITG）擔任機構博士後研究員。目前，他在印度泰米爾納德邦維洛爾科技學院的數學系擔任助理教授，擁有六年的教學經驗。他的研究領域包括分形分析、分形插值函數、分數微積分、非線性動力學和氣候變化。他已在多個知名國際期刊上發表超過40篇研究文章。他成功出版了三本書，分別由以下出版社發行：CRC Press（2019年）、Springer: Complexity（2021年）和SpringerBriefs in Complexity（2024年）。他曾擔任CRC Press和Taylor & Francis Group的兩本編輯書籍的編輯。他還擔任《歐洲物理期刊特刊》的兩個特刊的客座編輯。他目前擔任超過10本國際期刊的審稿人，並獲得了“2021年傑出EPJ審稿人”的稱號。最近，他獲得了印度政府SERB的TARE獎學金，為期2024年至2026年。

Kishore Bingi於2012年獲得印度阿查里亞納加爾朱納大學的電氣與電子工程學士學位。2014年，他在印度卡利庫特國立技術學院獲得儀器與控制系統的碩士學位，並於2019年在馬來西亞的國油科技大學獲得電氣與電子工程的博士學位。2014年至2015年，他在印度塔塔顧問服務有限公司擔任助理系統工程師。2019年至2020年，他在國油科技大學擔任研究科學家和博士後研究員。2020年至2022年，他在維洛爾科技學院的過程控制實驗室擔任助理教授。自2022年以來，他在馬來西亞國油科技大學的電氣與電子工程系擔任教職。他的研究領域包括開發分數階神經網絡、分數階系統和控制器、混沌預測與預報，以及先進的混合優化技術。他是IEEE和IET的會員，並且是英國工程委員會註冊的特許工程師（CEng）。他擔任《應用數學與計算機科學國際期刊》的編輯委員會成員，以及《工程中的數學問題》和《控制科學與工程期刊》的學術編輯。

Cristina Serpa擁有應用數學（基礎應用）的學位，並在里斯本大學科學學院獲得數學碩士和博士學位，專攻數學分析。她是里斯本理工學院高等工程學院數學系的受邀教授。她的教學工作通常集中在工程的微積分課程單元上。她是里斯本大學數學、基礎應用與運籌研究中心（CMAFcIO）的成員，並與葡萄牙數學學會合作。她在分形的基礎理論層面及其應用背景下進行研究。她創建了分形回歸方法，並開發了相應的軟體以從實際數據中獲得分形函數。