Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting

by Eugene M. Izhikevich

Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. 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.

Genres: Neuroscience, Science, Mathematics, Biology, Textbooks, Technical, Physics

460 pages, Kindle Edition

First published November 1, 2006

Reviews

[Michael Weaver · Rating 5 out of 5]

This is a great book giving the foundation for nonlinear dynamical systems in neuroscience. It sheds light on understanding of how the dynamics of neurons work, which was great for me becasue it is a subject I have been wanting to learn more about for a while now. This book gave me a great place to start.

[nika]

tentatively marking this as read otherwise it'll sit in my 'currently-reading' books forever. i'll admit that at least 70% of this book is way beyond what i understand and/or need at the moment, but i'll definitely be coming back to this, because it has some great explanations and illustrations

[DJ]

Holy hadron! A dynamical systems book focusing on the brain! Sometimes the world writes books just for me...

[Will Dorrell · Rating 4 out of 5]

Theoretical Neuroscience textbook about neuron models and non-linear dynamics.

This is a great book.

I read parts of it while revising for an exam, and I thought it gave a very clear and helpful guide to quite a large section of literature I'd never bumped into before. The driving idea (that neurons are excitable dynamical systems, and can be understood best using ideas from nonlinear dynamics) was great.

I don't tend to find this super biological stuff so engrossing, but it's just well done here.

[C. Hinsley · Rating 4 out of 5]

The only all-in-one resource on single-neuron dynamics for people who don't know have a PhD in neuroscience. Izhikevich gave a full classification of 2-slow-1-fast-dimension bursting emergence/cessation oscillatory bifurcation dynamics, and an exposition of those results is contained in the book. Some basic modeling (just Hodgkin-Huxley membrane dynamics & reduced chemical/electrical synapses, really; no cable theory, dendritic processing, geometry-aware modeling, neurotransmitter dissipation, etc.) is taught.

[Yates Buckley · Rating 5 out of 5]

Izhikevich writes a solid book about the mathematical stability of different neuron signalling patterns based on input. The book was a very clear read for me, helping me understand a fundamental character of the model for a firing neuron in the fashion of Hodgkin and Huxley's squid axon.
This is a technical text, but also a philosophical one in some aspects in that it opens the door to a new mathematical model approach to understanding the brain from a very broad perspective. The text does not adequately acknowledge its limitations regarding techniques. Ultimately dynamical systems analysis is more an educational approach than an engineering one, but valuable nevertheless.

[Alejandro Bandera · Rating 4 out of 5]

Solo me he leído el capítulo 9 sobre el Bursting para mi trabajo de Alumno Interno.
El capítulo está muy completo aunque he echado en falta la formulación matemática de cada caso ya que está solo aparece con algunos ejemplos en los ejercicios del capítulo.
Las imágenes están muy bien presentadas y se entienden a la perfección.

Probablemente vuelva a leerme el capítulo durante el año.

[Danilo Pozorovich · Rating 4 out of 5]

This book is a hard slog and very detailed but well worth the read. I have a couple of math degrees so the math wasn’t too bad but the neuroscience escaped me; nonetheless it is very well written and I recommend it

[Miguel V · Rating 5 out of 5]

Great book, even for starters, guides you through the amazing mathematics behind the modelling of neuron models, even though might seem hard to follow at first, just keep reading and you'll definitely find the way. Loved this book

[MT · Rating 5 out of 5]

informative and well-structured

[esteban · Rating 5 out of 5]

had to read for research extremely good book, an actual textbook that you can understand without having prior knowledge of neuroscience; but you do need to know differential equations. godsend

[Nick Black]

this looks like one of those things where you order a freakish book from MIT press on a humbug, and find out two weeks later you knew nothing about anything (see: Smil Vaclav. Energy in Nature and Society; see: Pierce Benjamin. Types and Programming Languages; etc.). hurrah! pretty cheap used, too!

[Katherine · Rating 5 out of 5]

I like the shade of green.

Good job!

[Katherine · Rating 5 out of 5]

I love this shade of green.

Good job!

[Eren Sezener · Rating 5 out of 5]

This is an extremely well written book. Even when compared to non-textbooks.

[Chris · Rating 5 out of 5]

Excellent introduction to Dynamical Systems theory and its application to Neuroscience. Gives many real world examples.