Brzychczy, Stanisław creator author. Poznanski, Roman R. author. text bibliography ne 2014 monographic eng

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xii, 188 pages : illustrations (some color) ; 24 cm Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables-such as synaptic or firing rate activity in populations of neurons -and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience. Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain. Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling. -- Stanisław Brzychczy, Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland, Roman R. Poznanski, Computation and Informatics Research Cluster, Instiutute of Research Management and Monitoring, University of Malaya, Kuala Lumpur, Malaysia. Includes bibliographical references (pages 175-185) and index. Computational neuroscience Neurosciences Mathematics Models, Neurological Computational Biology methods Neurosciences methods Nonlinear Dynamics Computational neuroscience Neurosciences Mathematics QP357.5 .B79 2014 612.80151 2013 I-797 WL 20 9780124114685 0124114687 2013444098 NLM 131107 20151120153525.0 17933692 eng