Two models analyzing the dynamics of adaptation algorithms

An approach to analysis of dynamics of adaptation algorithms is suggested. According to this approach the approximate models of the algorithm are constructed. It is shown that the role of model of an adaptation algorithm described by stochastic difference equations may be played by a common differential equation (a deterministic model) or a stochastic differential equation (a stochastic model). These models are applicated to studying of the dynamics of linear, sign, perceptron and random search algorithms.