By Paul C. Bressloff
Waves in Neural Media: From unmarried Neurons to Neural Fields surveys mathematical types of touring waves within the mind, starting from intracellular waves in unmarried neurons to waves of task in large-scale mind networks. The paintings presents a pedagogical account of analytical equipment for locating touring wave strategies of the diversity of nonlinear differential equations that come up in such versions. those contain general and singular perturbation tools, weakly nonlinear research, Evans features and wave balance, homogenization thought and averaging, and stochastic techniques. additionally lined within the textual content are specific equipment of resolution the place acceptable. traditionally conversing, the propagation of motion potentials has encouraged new arithmetic, fairly with reference to the PDE idea of waves in excitable media. extra lately, continuum neural box versions of large-scale mind networks have generated a brand new set of fascinating mathematical questions with reference to the answer of nonlocal integro-differential equations.
Advanced graduates, postdoctoral researchers and college operating in mathematical biology, theoretical neuroscience, or utilized nonlinear dynamics will locate this publication to be a priceless source. the most necessities are an introductory graduate path on traditional differential equations or partial differential equations, making this an available and certain contribution to the sector of mathematical biology.
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