Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Computational Neuroscience) [Hardcover]

Eugene M. Izhikevich (Author)

Book Description

ISBN-10: 0262090430 | ISBN-13: 978-0262090438 | Publication Date: November 1, 2006 | Edition: 1

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 systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology.

Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, 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 continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, 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 department 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.

Editorial Reviews

Review

"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 understanding of the utility of nonlinear dynamics applied to biology."
—Bard Ermentrout, Department of Mathematics, University of Pittsburgh

"A stimulating, entertaining, and scenic tour of neuronal modeling from a nonlinear dynamics viewpoint."
—John Rinzel, Center for Neural Science and Courant Institute, New York University

About the Author

Eugene M. Izhikevich is Chairman and CEO of Brain Corporation in San Diego and was formerly Senior Fellow in Theoretical Neurobiology at the Neurosciences Institute, San Diego. He is editor-in-chief of Scholarpedia, the free peer-reviewed encyclopedia.

Product Details

• Hardcover: 457 pages
• Publisher: The MIT Press; 1 edition (November 1, 2006)
• Language: English
• ISBN-10: 0262090430
• ISBN-13: 978-0262090438
• Product Dimensions: 10.1 x 7.2 x 1.1 inches
• Shipping Weight: 2.2 pounds
• Average Customer Review: 4.9 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #894,756 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

20 of 20 people found the following review helpful:

5.0 out of 5 stars An Interesting Book on Spiking Mechanism and Nonlinear Dynamical System, August 10, 2007

By 

Man Kam Tam (Calexico, CA USA) - See all my reviews
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This review is from: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Computational Neuroscience) (Hardcover)

The goal of Izhikevich's book is to study "the relationship between electrophysiology, bifurcations, and computational properties of neurons." The book also introduces the fundamental concepts of nonlinear dynamical system such as (1) equilibrium, (2) stability, (3) limit cycle attractor, and (4) bifurcations. Actually, it is a good introductory book on applying nonlinear dynamical system on scientific research. The primary subject of the book is the spiking (excitability and bursting) of neurons. By utilizing graphs or phase portraits to demonstrate the mechanism of the spiking generation of neurons, the author makes the readers understand both the spiking mechanism and the concepts of nonlinear dynamical system with ease.

13 of 13 people found the following review helpful:

5.0 out of 5 stars So you think you are afraid of some math?, October 24, 2007

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Robert Butera (Pine Lake, GA) - See all my reviews
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This review is from: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Computational Neuroscience) (Hardcover)

This book encapsulates in a single text a large body of knowledge by the author and others over the past two decades on the use of geometrical techniques to both classify and study a large range of single neuron models. While much of this material is known to "experts" in the field, the value of this text is i1) teaching this dynamical systems perspective on single neuron dynamics to generations of new students and 2) educating non-mathematicians into both the utility and use of these theories. Many other texts and papers on this topic leave non-mathematicians "in the dust" shortly after the introduction, but Eugene's excellent use of figures to explain concepts geometrically as well as mathematically enables a PhD student in engineering or quantitative biology to fully appreciate what is going on, not to mention seasoned experimentalists.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Amazing Book, May 8, 2011

By 

Ghassan Ayesh (Cupertino, CA) - See all my reviews
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This review is from: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting (Computational Neuroscience) (Paperback)

This book will teach you the dynamics of neurons, how to model the dynamics of neurons, complex systems modeling and how our understanding of the spiking neural systems came. This is a prize in every way. The book is engaging and easy to follow - well to some extent given the advanced topic the author is engaging the readers with. I am impressed of the ease the author applies non linear dynamical systems theory modeling techniques at ease in order to come up with a neural model that the author Izhikevich evolves throughout the chapters of the book, with clear schematics in every chapter which visually explain the modeling as well. Superb indeed. The subject overall is not an easy topic to attack or explain but Izhikevich is up for the challenge.