000			03860nam a22005295i 4500
001			978-1-4614-8866-8
003			DE-He213
005			20140220082503.0
007			cr nn 008mamaa
008			131017s2014 xxu| s |||| 0|eng d
020			_a9781461488668 _9978-1-4614-8866-8
024	7		_a10.1007/978-1-4614-8866-8 _2doi
050		4	_aQA76.87
072		7	_aPBWH _2bicssc
072		7	_aMAT003000 _2bisacsh
082	0	4	_a519 _223
100	1		_aBressloff, Paul C. _eauthor.
245	1	0	_aWaves in Neural Media _h[electronic resource] : _bFrom Single Neurons to Neural Fields / _cby Paul C. Bressloff.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2014.
300			_aXIX, 436 p. 151 illus., 18 illus. in color. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aLecture Notes on Mathematical Modelling in the Life Sciences, _x2193-4789
505	0		_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.
520			_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.
650		0	_aMathematics.
650		0	_aNeurosciences.
650		0	_aDifferential Equations.
650		0	_aPhysiology _xMathematics.
650		0	_aDistribution (Probability theory).
650	1	4	_aMathematics.
650	2	4	_aMathematical Models of Cognitive Processes and Neural Networks.
650	2	4	_aPhysiological, Cellular and Medical Topics.
650	2	4	_aNeurosciences.
650	2	4	_aMathematical and Computational Biology.
650	2	4	_aProbability Theory and Stochastic Processes.
650	2	4	_aOrdinary Differential Equations.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461488651
830		0	_aLecture Notes on Mathematical Modelling in the Life Sciences, _x2193-4789
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-8866-8
912			_aZDB-2-SMA
999			_c92265 _d92265