An Introduction to the Mathematics of Neurons
Modeling in the Frequency Domain

Describes signal processing aspects of neural networks and their applications. This is an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Frank C. Hoppensteadt (Author)

9780521590754, Cambridge University Press

Hardback, published 28 June 1997

232 pages, 69 b/w illus. 1 table
23.7 x 15.8 x 2.4 cm, 0.493 kg

"...a brief and nice introduction to the mathematical methods and models used in the theory of neural networks and their applications." Monatshefte fur Mathematik

This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.

Preface
1. Some useful electrical circuits
2. A theory of simple clocks
3. Some mathematical models of neurons
4. Signal processing in phase-locked systems
5. Small physiological control networks
6. Memory, phase change, and synchronization
7. Attention and other brain phenomena
Appendices
References
Index.

Subject Areas: Mathematical modelling [PBWH]