This volume introduces some basic theories on computational neuroscience. Chapter 1 is a brief introduction to neurons, tailored to the subsequent chapters. Chapter 2 is a self-contained introduction to dynamical systems and bifurcation theory, oriented towards neuronal dynamics. The theory is illustrated with a model of Parkinson's disease. Chapter 3 reviews the theory of coupled neural oscillators observed throughout the nervous systems at all levels; it describes how oscillations arise, what pattern they take, and how they depend on excitory or inhibitory synaptic connections. Chapter 4 specializes to one particular neuronal system, namely, the auditory system. It includes a self-contained introduction, from the anatomy and physiology of the inner ear to the neuronal network that connects the hair cells to the cortex, and describes various models of subsystems.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
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Alla Borisyuk Avner Friedman Bard Ermentrout David Terman
Tutorials in Mathematical Biosciences I Mathematical Neuroscience
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Authors Alla Borisyuk Mathematical Biosciences Institute The Ohio State University 231 West 18th Ave. Columbus, OH 43210-1174, USA e-mail:
[email protected]
Avner Friedman Mathematical Biosciences Institute The Ohio State University 231 West 18th Ave. Columbus, OH 43210-1174, USA e-mail:
[email protected]
Bard Ermentrout Department of Mathematics University of Pittsburgh 502 Thackeray Hall Pittsburgh, PA 15260, USA e-mail: