Neurodynamics: An Applied Mathematics Perspective

Coombes, Stephen, Wedgwood, Kyle C. a.

Neurodynamics: An Applied Mathematics Perspective
  • 出版商: Springer
  • 出版日期: 2024-05-11
  • 售價: $2,480
  • 貴賓價: 9.5 折 $2,356
  • 語言: 英文
  • 頁數: 507
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303121918X
  • ISBN-13: 9783031219184

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商品描述

This book is about the dynamics of neural systems and should be suitable for those with a background in mathematics, physics, or engineering who want to see how their knowledge and skill sets can be applied in a neurobiological context. No prior knowledge of neuroscience is assumed, nor is advanced understanding of all aspects of applied mathematics! Rather, models and methods are introduced in the context of a typical neural phenomenon and a narrative developed that will allow the reader to test their understanding by tackling a set of mathematical problems at the end of each chapter. The emphasis is on mathematical- as opposed to computational-neuroscience, though stresses calculation above theorem and proof. The book presents necessary mathematical material in a digestible and compact form when required for specific topics. The book has nine chapters, progressing from the cell to the tissue, and an extensive set of references. It includes Markov chain models for ions, differential equations for single neuron models, idealised phenomenological models, phase oscillator networks, spiking networks, and integro-differential equations for large scale brain activity, with delays and stochasticity thrown in for good measure. One common methodological element that arises throughout the book is the use of techniques from nonsmooth dynamical systems to form tractable models and make explicit progress in calculating solutions for rhythmic neural behaviour, synchrony, waves, patterns, and their stability. This book was written for those with an interest in applied mathematics seeking to expand their horizons to cover the dynamics of neural systems. It is suitable for a Masters level course or for postgraduate researchers starting in the field of mathematical neuroscience.

商品描述(中文翻譯)

這本書探討神經系統的動態，適合具備數學、物理或工程背景的讀者，希望看到他們的知識和技能如何應用於神經生物學的背景中。不需要先備的神經科學知識，也不需要對應用數學的所有方面有高深的理解！相反，模型和方法是在典型的神經現象背景下介紹的，並且通過在每章結尾處解決一組數學問題來發展敘述，讓讀者能夠測試他們的理解。重點是數學神經科學，而不是計算神經科學，儘管計算在定理和證明之上。在特定主題需要時，書中以易於理解和簡潔的形式呈現必要的數學材料。本書共有九章，從細胞到組織，並提供了大量的參考文獻。其中包括用於離子的馬爾可夫鏈模型，用於單個神經元模型的微分方程，理想化的現象學模型，相位振盪器網絡，尖峰網絡，以及用於大規模腦活動的積分微分方程，其中包括延遲和隨機性。貫穿整本書的一個常見方法論元素是使用非光滑動力系統的技術來形成易處理的模型，並在計算節奏神經行為、同步、波紋、模式及其穩定性的解決方案方面取得明確進展。本書是為對應用數學感興趣並希望擴展視野以涵蓋神經系統動態的讀者而寫的。適合碩士課程或從事數學神經科學領域的研究生研究者使用。

作者簡介

Stephen Coombes is a Professor of Applied Mathematics at the University of Nottingham, UK. His research interest is in the use of nonlinear dynamics to understand aspects of the human central nervous system. He has co-edited two books and authored over 120 peer-reviewed journal articles. He has supervised 22 PhD students and 8 postdoctoral fellows.Together with colleagues in Mathematics and Neuroscience he is actively pursuing research projects ranging from single cell dynamics to neuronal circuits to whole-brain dynamics with applications in psychology, neuroimaging, medicine, and psychiatry.

Kyle Wedgwood is a Lecturer in Mathematics in the Living Systems Institute at the University of Exeter, UK. He applies techniques from dynamical systems theory to understand how electrically excitable cells produce coherent rhythms in networks and has authored 22 peer-reviewed journal articles. He currently supervises 4 PhD students and 2 postdoctoral fellows. In his current research, he is exploring how mathematics can be embedded in neuroscience experiments.

作者簡介(中文翻譯)

Stephen Coombes是英國諾丁漢大學應用數學教授。他的研究興趣在於利用非線性動力學來理解人類中樞神經系統的各個方面。他共同編輯了兩本書並撰寫了超過120篇同行評審的期刊文章。他指導了22名博士生和8名博士後研究員。與數學和神經科學的同事們一起，他積極從單個細胞動力學到神經元回路再到整個大腦動力學的研究項目，並應用於心理學、神經影像學、醫學和精神病學。

Kyle Wedgwood是英國埃克塞特大學生命系統研究所的數學講師。他應用動力系統理論的技術，來理解可電激動細胞在網絡中如何產生一致的節奏，並撰寫了22篇同行評審的期刊文章。他目前指導了4名博士生和2名博士後研究員。在他目前的研究中，他正在探索如何將數學嵌入神經科學實驗中。

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