Spatial Dynamics and Pattern Formation in Biological Populations
暫譯: 生物族群中的空間動力學與模式形成

本書介紹了生態學、流行病學和神經系統中確定性（以及一些隨機性）時空現象的建模。書中提供了這些領域的經典模型調查及其最新應用。

本書首先詳細描述了空間動力學/擴散過程如何影響生物種群的動態。這些過程在理解疫情的爆發和擴散中扮演著關鍵角色，幫助我們從公共衛生的角度設計控制策略。書中簡要討論了大腦的功能機制（單神經元模型和網絡層級），以及經典的神經動力學模型在空間和時間中的應用。相關現象及生態學、流行病學和神經科學中現有的建模方法被介紹，這些方法提供了這些模型中模式形成的例子。對模式的分析使我們能夠研究潛在系統的宏觀和微觀行為的動態，以及在擴散系統中觀察到的行進波型模式。接著，作者對病毒動力學進行了詳細分析，涵蓋了不同類型的傳染病模型，包括兩個流感模型、五個埃博拉病毒模型和七個寨卡病毒模型，並考慮了擴散和時間延遲。專門有一章致力於研究大腦動力學（時空中的神經系統）。

本書展示了在反應-擴散系統建模方面取得的重大進展，並回顧了系統中的時空模式形成。書中介紹了適當的數學模型的發展和詳細分析（如線性穩定性、弱非線性分析、分岔分析、控制理論、數值模擬）。

主要特點：

- 涵蓋分析生物種群反應-擴散模型所需的基本概念和數學技能。
- 以易於理解的方式介紹概念，使具備基本微分方程和數值方法知識的讀者能夠理解分析。結果也用圖形進行說明。
- 專注於使用基本概念和經典模型進行數學建模和數值模擬，涵蓋種群動力學、病毒和大腦動力學。
- 涵蓋使用空間和非空間方法的廣泛模型。
- 涵蓋來自生態學的單一、雙重和多物種反應-擴散模型以及生物化學模型。對模型進行穩定性分析，包括平衡點的穩定性、圖靈不穩定性、霍普夫分岔和模式形成。
- 使用Mathematica進行問題解決，使用MATLAB進行模式形成。
- 包含已解的範例和練習題。

本書適合高年級本科生、研究生和研究學生。對於在上述領域工作的人士，本書提供了最新研究的資訊。文本呈現了建立模型和進行分析所需的所有基本概念和數學技能。

Dr. Ranjit Kumar Upadhyay is a Professor in the Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, India. He is an acknowledged researcher and has contributed in various areas of Applied Mathematics, Mathematical modeling and Nonlinear Dynamics. His research areas are interdisciplinary in nature like dynamical systems theory; chaotic dynamics of real-world situations; population dynamics for marine and terrestrial ecosystems; spatial dynamics in epidemic (influenza, Ebola and Zika viruses), e-epidemic and neural models; and reaction-diffusion modeling. He has published 150 research papers in different International Journals of repute and a number of these publications are with international collaborators. He has supervised 9 students for their Ph.D. Currently, 6 students are working under his guidance for their Ph.D. degree. He has handled a number of sponsored R&D projects. He is the co-author of the Book titled "Introduction to Mathematical Modeling and Chaotic Dynamics" published by Taylor & Francis group (CRC Press, USA). He is on the Editorial Board for many reputed Journals. He is an Associate Editor of the Elsevier Journal "Food Webs" and Springer Journal "Advances in Difference Equations" and "Differential Equations and Dynamical Systems". He is a Guest Editor of a Special Issue entitled "Nonlinear Models in Biosignaling, Biosensor and Neural Systems - Modeling, Simulations, and Applications" being brought out by the Springer Journals "Differential Equations and Dynamical Systems". He was a visiting research fellow under the Indo-Hungarian Educational exchange program in Eötvös University, Budapest, Hungary. He was a visiting scientist and delivered invited lectures in many renowned institutions like University of Cambridge; University of Leicester, UK; University of Le Havre Normandie, France. He is a member of the International Society of Computational Ecology, Hong Kong.

Dr. Satteluri R. K. Iyengar was a Professor and former Head of the Department of Mathematics, Indian Institute of Technology (IIT), New Delhi, India. He worked as a Professor for more than 22 years. His areas of research work are Numerical Analysis and Mathematical Modeling. He is the co-author of the Books titled (a) "Introduction to Mathematical Modeling and Chaotic Dynamics" published by Taylor & Francis group (CRC Press, USA), and (b) "Advanced Engineering Mathematics", published by Narosa Publishing House. He is a co-author of a number of books on Numerical Analysis like "Numerical Methods for Scientific and Engineering Computation" etc. He has many research publications in International Journals of repute. He was a post-doctoral fellow at Oxford University Computing Laboratory, Oxford, United Kingdom, and the University of Saskatchewan, Canada. He was awarded the Distinguished Service Award by the Indian Institute of Technology, New Delhi, India during its Golden Jubilee Year in 2011. He was also awarded the Distinguished Indian Award in 2007 by the Pentagram Research Center (P) Limited, Hyderabad, India for his contributions.

Dr. Ranjit Kumar Upadhyay 是印度達漢巴德印度科技學院（Indian School of Mines）數學與計算系的教授。他是一位公認的研究者，對應用數學、數學建模和非線性動力學等多個領域做出了貢獻。他的研究領域具有跨學科特性，包括動態系統理論；現實世界情況的混沌動力學；海洋和陸地生態系統的人口動態；流行病（流感、埃博拉和茲卡病毒）的空間動態、電子流行病和神經模型；以及反應-擴散建模。他在多個國際知名期刊上發表了150篇研究論文，其中許多與國際合作者共同發表。他已指導9名學生獲得博士學位，目前有6名學生在他的指導下攻讀博士學位。他處理了多個贊助的研發項目。他是由Taylor & Francis集團（CRC Press, USA）出版的書籍《Introduction to Mathematical Modeling and Chaotic Dynamics》的共同作者。他是多本知名期刊的編輯委員會成員。他是Elsevier期刊《Food Webs》和Springer期刊《Advances in Difference Equations》及《Differential Equations and Dynamical Systems》的副編輯。他是Springer期刊《Differential Equations and Dynamical Systems》特刊《Nonlinear Models in Biosignaling, Biosensor and Neural Systems - Modeling, Simulations, and Applications》的客座編輯。他曾在匈牙利厄爾特大學（Eötvös University）擔任印度-匈牙利教育交流計畫的訪問研究員。他曾是訪問科學家，並在劍橋大學、英國萊斯特大學、法國勒阿弗爾大學等多所知名機構發表邀請講座。他是國際計算生態學會的成員，總部位於香港。

Dr. Satteluri R. K. Iyengar 曾是印度新德里印度科技學院（IIT）的數學系教授及前系主任。他擔任教授超過22年。他的研究領域包括數值分析和數學建模。他是由Taylor & Francis集團（CRC Press, USA）出版的書籍《Introduction to Mathematical Modeling and Chaotic Dynamics》及Narosa Publishing House出版的《Advanced Engineering Mathematics》的共同作者。他還是多本有關數值分析的書籍的共同作者，如《Numerical Methods for Scientific and Engineering Computation》等。他在多個國際知名期刊上發表了許多研究論文。他曾在英國牛津大學計算實驗室和加拿大薩斯喀徹溫大學擔任博士後研究員。他在2011年印度科技學院金禧年期間獲得了傑出服務獎。他還於2007年獲得印度Hyderabad的Pentagram Research Center (P) Limited頒發的傑出印度獎，以表彰他的貢獻。