Synopses & Reviews
Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.
This book develops the bifurcation theory for weakly connected neural networks. The authors analyze the relationship between synaptic organizations (anatomy) and dynamical properties (function) of the brain. In particular the authors show that there are some synaptic organizations that have especially rich dynamic behavior.
Includes bibliographical references (p. -393) and index.
Table of Contents
On the Application of Kalman Filtering to Correct Errors due to Vertical Deflection in Inertial Navigation.
- Filtering and Detection Problems for Nonlinear Time Series.
- Spectral and Bispectral Methods for the Analysis of Nonlinear (Non-Gaussian) Time-Series Signals.
- Bilinear Time Series: Theory and Application.
- Bivariate Bilinear Models and Their Identification.
- Nonlinear Time Series Modelling in Population Biology.
- The Akaike Information Criterion in Threshold Modelling.
- Nonlinear Time Series Analysis for Dynamical Systems of Catastrophe Type.
- Nonlinear Processing with M-th Order Signals.
- Stochastic Circulatory Lymphocyte Models.