Eugene M. Izhikevich's Books

Dynamical Systems in Neuroscience

The Geometry of Excitability and Bursting

By: Eugene M. Izhikevich

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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. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

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Page Count

459

Publisher

MIT Press

Published Date

ISBN 10

0262514206

ISBN 13

9780262514200

Weakly Connected Neural Networks

By: Frank C. Hoppensteadt,Eugene M. Izhikevich

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Weakly Connected Neural Networks

By: Frank C. Hoppensteadt,Eugene M. Izhikevich

Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.

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Page Count

404

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461218284

ISBN 13

9781461218289

Dynamical Systems in Neuroscience

The Geometry of Excitability and Bursting

By: Eugene M. Izhikevich

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Dynamical Systems in Neuroscience

The Geometry of Excitability and Bursting

By: Eugene M. Izhikevich

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

459

Publisher

MIT Press

Published Date

ISBN 10

0262514206

ISBN 13

9780262514200

Book's by Eugene M. Izhikevich

Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience

Weakly Connected Neural Networks

Weakly Connected Neural Networks

Dynamical Systems in Neuroscience

Dynamical Systems in Neuroscience

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