Freshly Printed - allow 10 days lead
Couldn't load pickup availability
Mathematical Neuroscience
The first research monograph in mathematical neuroscience devoted exclusively to the theory and methods of nonlinear analysis of infinite systems
Stanislaw Brzychczy (Author), Roman R. Poznanski (Author)
9780124114685, Elsevier Science
Hardback, published 30 September 2013
208 pages
23.4 x 19 x 2 cm, 0.62 kg
"Brzychczy,… Kraków and Poznanski…present methods of nonlinear functional analysis and their application to neuroscience. This is the first book, they say, to compile methods of nonlinear analysis to better understand the dynamics associated with solutions of infinite systems of equations. It would be suitable as a textbook for a one-semester graduate course in mathematical neuroscience for neuroscience students seeking tools and mathematics students looking for applications." --Reference & Research Book News, December 2013
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.
Part I. Methods of Nonlinear Analysis 1. Introduction to Part I 2. Notations, Definitions and Assumptions 3. Differential Inequalities 4. Monotone Iterative Methods 5. Methods of Lower and Upper Solutions 6. Truncation Method 7. Fixed Point Method 8. Stability of Solutions PART II. Application of Nonlinear Analysis 9. Introduction to Part II 10. Continuous and Discrete Models of Neural Systems 11. Nonlinear Cable Equations 12. Reaction-Diffusion Equations Appendix Further Reading
Subject Areas: Neurosciences [PSAN], Neurology & clinical neurophysiology [MJN]
