"Waves in Neural Media: From Single Neurons to Neural Fields"
surveys mathematical models of traveling waves in the brain,
ranging from intracellular waves in single neurons to waves of
activity in large-scale brain networks. The work provides a
pedagogical account of analytical methods for finding traveling
wave solutions of the variety of nonlinear differential equations
that arise in such models. These include regular and singular
perturbation methods, weakly nonlinear analysis, Evans functions
and wave stability, homogenization theory and averaging, and
stochastic processes. Also covered in the text are exact methods of
solution where applicable. Historically speaking, the propagation
of action potentials has inspired new mathematics, particularly
with regard tothe PDE theory of waves in excitable media. More
recently, continuum neural field models of large-scale brain
networks have generated a new set of interesting mathematical
questions with regard tothe solution of nonlocal
integro-differential equations.
Advanced graduates, postdoctoral researchers and faculty working
in mathematical biology, theoretical neuroscience, or applied
nonlinear dynamics will find this book to be a valuable resource.
The main prerequisites are an introductory graduate course on
ordinary differential equations or partial differential equations,
making this an accessible and unique contribution to the field of
mathematical biology."
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