Mathematical Neuroscience, 1st Edition

  • Published By:
  • ISBN-10: 0124104827
  • ISBN-13: 9780124104822
  • DDC: 612.8
  • Grade Level Range: College Freshman - College Senior
  • 208 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Half Title Page.
Title Page.
Copyright Page.
About the Authors.
1: Methods of Nonlinear Analysis.
2: Introduction to Part I.
3: Preliminary Considerations.
4: Differential Inequalities.
5: Monotone Iterative Methods.
6: Methods of Lower and Upper Solutions.
7: Truncation Method.
8: Fixed Point Method.
9: Stability of Solutions.
10: Application of Nonlinear Analysis.
11: Introduction to Part II.
12: Continuous and Discrete Models of Neural Systems.
13: Nonlinear Cable Equations.
14: Reaction-Diffusion Equations.
Further Reading.