LEADER 03362oam  2200457   450 
001 9910299962103321
005 20190911103512.0
010   $a1-4614-8866-4
024 7 $a10.1007/978-1-4614-8866-8
035   $a(OCoLC)863045384
035   $a(MiFhGG)GVRL6YOM
035   $a(EXLCZ)992550000001151147
100   $a20130819d2014      uy             0
101 0 $aeng
135   $aurun|---uuuua
181   $ctxt
182   $cc
183   $acr
200 10$aWaves in neural media $efrom single neurons to neural fields /$fPaul C. Bressloff
205   $a1st ed. 2014.
210  1$aNew York :$cSpringer,$d2014.
215   $a1 online resource (xix, 436 pages) $cillustrations (some color)
225 1 $aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4789
300   $a"ISSN: 2193-4789."
300   $a"ISSN: 2193-4797 (electronic)."
311   $a1-4614-8865-6 
320   $aIncludes bibliographical references and index.
327   $aPreface -- Part I Neurons -- Single Neuron Modeling -- Traveling Waves in One-Dimensional Excitable Media -- Wave Propagation Along Spiny Dendrites -- Calcium Waves and Sparks -- Part II Networks -- Waves in Synaptically-Coupled Spiking Networks -- Population Models and Neural Fields -- Waves in Excitable Neural Fields -- Neural Field Model of Binocular Rivalry Waves -- Part III Development and Disease -- Waves in the Developing and the Diseased Brain -- Index.
330   $aWaves in Neural Media: From Single Cells to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations.  Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations and partial differential equations, making this an accessible and unique contribution to the field of mathematical biology. .
410  0$aLecture notes on mathematical modelling in the life sciences.
606   $aNeural networks (Neurobiology)
615  0$aNeural networks (Neurobiology)
676   $a006.3
676   $a006.32
700   $aBressloff$b Paul C$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721730
801  0$bMiFhGG
801  1$bMiFhGG
906   $aBOOK
912   $a9910299962103321
996   $aWaves in neural media$91410729
997   $aUNINA