Neural models of arbitrary chaotic systems: construction and the role of time delayed feedback in control and synchronization

摘要: This paper proposes a simple methodology to construct an iterative neural network which mimics given chaotic time series. The uses the Gamma test identify suitable (possibly irregular) embedding of series from one step predictive model may be constructed. A one-step is then constructed as feedforward trained using BFGS method. iterated produce close approximation original dynamics. We show how dynamics stabilized time-delayed feedback. Delayed feedback attractive method control because it has very low computational overhead and easy integrate into hardware systems. It also plausible for stabilization in biological Using delayed control, activated presence stimulus, such networks can behave associative memory, act recognition corresponds onto unstable periodic orbit. Surprisingly we find that response systems remarkably robust noise. briefly investigate stability proposed whilst control/synchronisation methods are not always stable classical sense they instead probabilistically locally stable. two independent copies synchronized variations Although less biologically plausible, these techniques have interesting applications secure communications.