Non-Linear Modelling and Chaotic Neural Networks

This paper proposes a simple methodology to construct an iterative neural network which mimics a given chaotic time series. The methodology uses the Gamma test to identify a suitable (possibly irregular) embedding of the chaotic time series from which a one step predictive model may be constructed. This model is then iterated to produce a close approximation to the original chaotic dynamics. Having constructed such networks we show how the chaotic dynamics may be stabilised using time-delayed feedback, which is a plausible method for stabilisation in biological neural systems. Using delayed feedback control, which is activated in the presence of a stimulus, such networks can behave as an associative memory, in which the act of recognition corresponds to stabilisation onto an unstable periodic orbit. We briefly illustrate how two identical dynamically independent copies of such a chaotic iterative network may be synchronised using the delayed feedback method. Although less biologically plausible, these techniques may have interesting applications in secure communications.