"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.
The first focused introduction to the use of nonlinear analysis
with an infinite dimensional approach to theoretical
neuroscienceCombines functional analysis techniques with nonlinear
dynamical systems applied to the study of the brainIntroduces
powerful mathematical techniques to manage the dynamics and
challenges of infinite systems of equations applied to neuroscience
modeling"
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