Product Description
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.

CUSTOMER REVIEWS (Average Customer Rating: 4.5 based on 3 reviews)

Book on the dynamcis of neurons

This book gives an understanding of how the dynamics of neurons work. It gives an insight to many different types of models. However, you would require a neuroscience background before understanding it more in depth.
May 21, 2008

So you think you are afraid of some math?

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.
October 24, 2007

An Interesting Book on Spiking Mechanism and Nonlinear Dynamical System

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.
August 10, 2007

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