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
ac
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
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