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English
Academic Press Inc
22 August 2013
Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics.

Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling.

By:   ,
Imprint:   Academic Press Inc
Country of Publication:   United States
Dimensions:   Height: 234mm,  Width: 191mm,  Spine: 18mm
Weight:   620g
ISBN:   9780124114685
ISBN 10:   0124114687
Pages:   208
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Hardback
Publisher's Status:   Active

Roman R. Poznanski is a distinguished mathematical neuroscientist and research professor in theoretical studies on the brain. As a prolific writer, he has edited several contemporary books: Biophysical Neural Networks (2001), Modeling in the Neurosciences (1999, 2005), Biophysics of Consciousness (2017), and co-authored Mathematical Neuroscience (2014).

Reviews for Mathematical Neuroscience

Brzychczy,... Krakow and Poznanski...present methods of nonlinear functional analysis and their application to neuroscience. This is the first book, they say, to compile methods of nonlinear analysis to better understand the dynamics associated with solutions of infinite systems of equations. It would be suitable as a textbook for a one-semester graduate course in mathematical neuroscience for neuroscience students seeking tools and mathematics students looking for applications. --Reference & Research Book News, December 2013


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