A Bifurcation Theory Approach To Learning And The Nonlinear Dynamics Of Pattern Formation And Pattern Recognition In Neural Network Models Of The Olfactory System

A Bifurcation Theory Approach to Learning and the Nonlinear Dynamics of Pattern Formation and Pattern Recognition in Neural Network Models of the Olfactory System

Neurodynamics - Proceedings Of The 9th Summer Workshop

This volume presents applications of mathematical techniques for modelling and performance analysis of neural networks. The collection of articles is motivated by the observation that the theory of neural network dynamics, i.e. Neurodynamics, still has to be given a thorough mathematical foundation. Therefore, the volume comprises research work on different mathematical approaches to neural networks; analytical and numerical techniques of dynamical systems theory, geometrical techniques, and methods of statistical physics. Articles analyse dynamics of neural netwroks in general or concentrate on specific network models of biological or neurocomputing origin. A few of the articles serve as a good introduction to these subjects.

Models of Wave Memory

This monograph examines in detail models of neural systems described by delay-differential equations. Each element of the medium (neuron) is an oscillator that generates, in standalone mode, short impulses also known as spikes. The book discusses models of synaptic interaction between neurons, which lead to complex oscillatory modes in the system. In addition, it presents a solution to the problem of choosing the parameters of interaction in order to obtain attractors with predetermined structure. These attractors are represented as images encoded in the form of autowaves (wave memory). The target audience primarily comprises researchers and experts in the field, but it will also be beneficial for graduate students.