Mathematical Neuroscience

Stanislaw Brzychczy

ISBN 10: 0124114687 / ISBN 13: 9780124114685

Editore: Elsevier Science Aug 2013, 2013

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This item is printed on demand - it takes 3-4 days longer - Neuware -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 208 pp. Englisch.

Codice articolo 9780124114685

Dati bibliografici

• Titolo: Mathematical Neuroscience
• Editore: Elsevier Science Aug 2013
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 0124114687
• ISBN 13: 9780124114685
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 244 L x 192 A x 17 P (millimetri) 244 millimetri di larghezza per 192 millimetri di altezza per 17 millimetri di profondità
• Peso: 603 grammi

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Riassunto

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

Informazioni sull?autore

Roman R. Poznanski develops theories in neuroscience with mathematics. He recently co-authored the book, "Mathematical Neuroscience." His passion remains to pinpoint and crack open complex problems holding back our understanding of how the brain works. He is adamant, that a new Einstein in neuroscience will one day produce a complete theory of the brain, not as a hodgepodge of models, but as an integrative theory expressed in terms of modern mathematics. He has over 20 years experience as a theoretician and modeller in the neurosciences. He has edited several contemporary books: Biophysical Neural Networks (2001) and Modeling in the Neurosciences (1999, 2005). He is currently a visiting professor at the Rockefeller University.