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### 动态系统在神经科学中的应用 #### 核心概念与理论背景《动态系统在神经科学》一书由尤金·伊日凯维奇（Eugene M. Izhikevich）撰写，深入探讨了动态系统理论如何应用于解释神经元活动的基本原理及其复杂行为。本书是计算神经科学领域的重要参考文献之一，着重于分析兴奋性和爆发性等关键现象的几何特性。 #### 兴奋性和爆发性的几何理解书中详细介绍了一种新的方法来理解神经元的兴奋性和爆发性，这被称为“兴奋性和爆发性的几何”。这种方法通过数学模型来描述神经元的行为，并利用相平面分析、分岔理论等工具来揭示神经元活动背后的动力学机制。例如，作者介绍了多种类型的神经元模型，包括经典的霍奇-赫胥黎模型以及简化版本如菲茨休-纳格莫模型等，这些模型有助于解析不同类型的神经元活动模式。 #### 计算神经科学的发展历程该书不仅关注理论层面的探索，还回顾了计算神经科学领域的历史发展。通过引用一系列经典著作和论文，伊日凯维奇展示了该领域是如何逐渐形成并发展的。这些参考资料覆盖了从20世纪90年代初到21世纪初的重要研究成果，包括： - **《电鱼中的神经网络》**：沃尔特·海利根伯格（Walter Heiligenberg）1991年的作品，研究了电鱼的神经系统。 - **《大脑的计算功能》**：帕特里夏·S·丘奇兰德（Patricia S. Churchland）和泰伦斯·J·塞杰诺夫斯基（Terrence J. Sejnowski）1992年的著作，探讨了大脑作为计算系统的功能。 - **《动态生物网络：胃肠道神经系统》**：罗纳德·M·哈里斯-瓦里克（Ronald M. Harris-Warrick）等人1992年编辑的书籍，聚焦于特定生物系统中的动态网络。 - **《神经网络的神经生物学》**：丹尼尔·加德纳（Daniel Gardner）1993年编辑的著作，探讨了神经网络的生物学基础。 - **《大脑中的大型神经理论》**：克里斯托夫·科赫（Christof Koch）和乔尔·L·戴维斯（Joel L. Davis）1994年编辑的书籍，汇集了关于大脑中大规模神经过程的研究成果。 - **《树突功能的理论基础：威尔弗里德·拉尔论文选集及评论》**：伊丹·西格尔（Idan Segev）等人1995年编辑的作品，收集了威尔弗里德·拉尔关于树突功能的重要论文。 - **《基底节的信息处理模型》**：詹姆斯·C·豪克（James C. Houk）等人1995年编辑的书籍，探讨了基底节区域的信息处理机制。 - **《尖峰：探究神经编码》**：弗雷德·里克（Fred Rieke）等人1997年的著作，讨论了神经元编码的原理。 - **《神经元、网络与运动行为》**：保罗·S·斯坦（Paul S. Stein）等人1997年编辑的书籍，研究了运动控制中的神经机制。 - **《神经元建模的方法：从离子通道到网络》**：克里斯托夫·科赫（Christof Koch）和伊丹·西格尔1998年第二版的作品，提供了神经元建模的技术指南。 - **《神经网络建模的基础：神经心理学与认知神经科学》**：兰道夫·W·帕克斯（Randolph W. Parks）等人1998年编辑的书籍，探讨了神经网络建模的心理学和认知科学基础。 - **《神经编码与分布式表征：神经计算的基础》**：劳伦斯·阿伯特（Laurence Abbott）和泰伦斯·J·塞杰诺夫斯基1999年编辑的作品，研究了神经编码和表征的原理。 - **《无监督学习：神经计算的基础》**：杰弗里·欣顿（Geoffrey Hinton）和泰伦斯·J·塞杰诺夫斯基1999年编辑的书籍，聚焦于无监督学习算法在神经计算中的应用。 - **《皮层回路中的快速振荡》**：罗杰·D·特劳布（Roger D. Traub）等人1999年的著作，研究了皮层回路中的高频振荡现象。 - **《计算视觉：感知与视觉行为中的信息处理》**：汉斯彼得·A·马洛特（Hanspeter A. Mallot）2000年的作品，探讨了视觉信息处理的计算模型。 - **《图形模型：神经计算的基础》**：迈克尔·I·乔丹（Michael I. Jordan）和泰伦斯·J·塞杰诺夫斯基2001年编辑的书籍，研究了图形模型在神经计算中的作用。 - **《自组织图谱形成：神经计算的基础》**：克劳斯·奥伯梅耶（Klaus Obermayer）和泰伦斯·J·塞杰诺夫斯基2001年编辑的作品，探讨了自组织图谱形成的原理。 - **《理论神经科学：神经系统的计算与数学建模》**：彼得·戴恩（Peter Dayan）和L. F. A. 阿伯特2001年的著作，全面介绍了理论神经科学的基本理论和方法。通过对这些著作的综述，可以看出计算神经科学是一个跨学科领域，它结合了数学、物理学、计算机科学等多个学科的知识和技术，旨在理解和模拟大脑的工作原理。伊日凯维奇的这本书为读者提供了一个深入了解动态系统理论如何应用于神经科学的机会，不仅对专业研究人员有重要的参考价值，也为广大爱好者打开了一个了解这一前沿领域的窗口。

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Dynamical Systems

in Neuroscience

Eugene M. Izhikevich

The Geometry of Excitability and Bursting

neuroscience/computational neuroscience

Dynamical Systems in Neuroscience

The Geometry of Excitability and Bursting

Eugene M. Izhikevich

In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must

call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical sys-

tems theory for researchers and graduate students in neuroscience. It also provides an overview of neu-

roscience for mathematicians who want to learn the basic facts of electrophysiology.

Dynamical Systems in Neuroscience presents a systematic study of the relationship of electro-

physiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information

processing in the brain depends not only on the electrophysiological properties of neurons but also on

their dynamical properties.

The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-

type models and going on to describe bursting systems. Each chapter proceeds from the simple to the

complex, and provides sample problems at the end. The book explains all necessary mathematical con-

cepts using geometrical intuition; it includes many figures and few equations, making it especially suit-

able for non-mathematicians. Each concept is presented in terms of both neuroscience and mathemat-

ics, providing a link between the two disciplines.

Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is

not a standard part of the graduate neuroscience curriculum—or taught by math or physics departments

in a way that is suitable for students of biology. This book offers neuroscience students and researchers

a comprehensive account of concepts and methods increasingly used in computational neuroscience.

An additional chapter on synchronization, with more advanced material, can be found at the author’s

website, www.izhikevich.com.

Eugene M. Izhikevich is Senior Fellow in Theoretical Neurobiology at the Neurosciences Institute, San

Diego, coauthor of

Weakly Conducted Neural Networks, and editor-in-chief of Scholarpedia, the free

peer-reviewed encyclopedia.

Computational Neuroscience series

“This book will be a great contribution to the subject of mathematical neurophysiology.”

—Richard Fitzhugh, former researcher, Laboratory of Biophysics, National Institutes of Health

“Eugene Izhikevich has written an excellent introduction to the application of nonlinear dynamics to the

spiking patterns of neurons. There are dozens of clear illustrations and hundreds of exercises ranging

from the very easy to Ph.D.-level questions. The book will be suitable for mathematicians and physicists

who want to jump into this exciting field as well as for neuroscientists who desire a deeper underst

and

ing of the utility of nonlinear dynamics applied to biology

.”

—Bard Ermentrout, Department of Mathematics, University of Pittsburgh

“

A stimulating, entert

aining, and scenic tour of neuronal modeling from a nonlinear dynamics viewpoint.

”

—John Rinzel, Center for Neural Science and Courant Institute, New Y

ork University

The MIT Press

Mass

husetts Institute of T

echnology

Cambridge, Massachusetts 02142

http://mitpress.mit.edu

0-262-09043-0

978-0-262-09043-8

Dynamical Systems in Neuroscience Izhikevich

49924Izhikevich 6/1/06 6:01 AM Page 1

Computational Neuroscience

Terrence J. Sejnowski and Tomaso A. Poggio, editors

Neural Nets in Electric Fish, Walter Heiligenberg, 1991

The Computational Brain, Patricia S. Churchland and Terrence J. Sejnowski, 1992

Dynamic Biological Networks: The Stomatogastric Nervous System, edited by Ronald M.

Harris-Warrick, Eve Marder, Allen I. Selverston, and Maurice Maulins, 1992

The Neurobiology of Neural Networks, edited by Daniel Gardner, 1993

Large-Scale Neuronal Theories of the Brain, edited by Christof Koch and Joel L. Davis, 1994

The Theoretical Foundations of Dendritic Function: Selected Papers of Wilfrid Rall with

Commentaries, edited by Idan Segev, John Rinzel, and Gordon M. Shepherd, 1995

Models of Information Processing in the Basal Ganglia, edited by James C. Houk, Joel L.

Davis, and David G. Beiser, 1995

Spikes: Exploring the Neural Code, Fred Rieke, David Warland, Rob de Ruyter van Stevenick,

and William Bialek, 1997

Neurons, Networks, and Motor Behavior, edited by Paul S. Stein, Sten Grillner, Allen I.

Selverston, and Douglas G. Stuart, 1997

Methods in Neuronal Modeling: From Ions to Networks, second edition, edited by Christof

Koch and Idan Segev, 1998

Fundamentals of Neural Network Modeling: Neuropsychology and Cognitive Neuroscience,

edited by Randolph W. Parks, Daniel S. Levin, and Debra L. Long, 1998

Neural Codes and Distributed Representations: Foundations of Neural Computation,edited

by Laurence Abbott and Terrence J. Sejnowski, 1999

Unsupervised Learning: Foundations of Neural Computation, edited by Geoﬀrey Hinton and

Terrence J. Sejnowski, 1999

Fast Oscillations in Cortical Circuits, Roger D. Traub, John G.R. Jeﬀerys, and Miles Al

Whittington, 1999

Computational Vision: Information Processing in Perception and Visual Behavior, Hanspeter

A. Mallot, 2000

Graphical Models: Foundations of Neural Computation, edited by Michael I. Jordan and

Terrence J. Sejnowski, 2001

Self-Organizing Map Formation: Foundation of Neural Computation, edited by Klaus Ober-

mayer and Terrence J. Sejnowski, 2001

Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems,

Peter Dayan and L. F. Abbott, 2001

Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Sys-

tems, Chris Eliasmith and Charles H. Anderson, 2003

The Computational Neurobiology of Reaching and Pointing, edited by Reza Shadmehr and

Steven P. Wise, 2005

Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, Eugene M.

Izhikevich, 2007

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