?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 to the 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 to the 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.
