Contributing Editor's Note: Application of neural network models to dynamical systems are not (of course) new. The classical example is the Hopfield network. The model proposed in the following work is a modified one. The authors consider a system when the presence of an external stimulus excites (activates) the control circuitry, which is otherwise inhibited. The control is switched on at the same time as the external signal is fed into the input line for stabilization.
Abstract: This paper proposes a simple methodology to construct an iterative neural network which mimics a given chaotic time series. This network is then iterated to produce a close approximation to the original chaotic dynamics. We then show how the chaotic dynamics may be stabilized using time-delayed feedback. Delayed feedback is an attractive method of control because it has a very low computational overhead (...).
> We also show how two independent copies of such a chaotic iterative network may be synchronized using variations of the delayed feedback method. Although less biologically plausible, these techniques may have interesting applications in secure communications.
- Neural Models Of Arbitrary Chaotic Systems: Construction And The Role Of Time Delayed Feedback In Control And Synchronization, A. J. Jones, A.P.M.Tsui & A. G.Oliveira, Complexity International, Draft Manuscript, October, 2001
- Contributed by Atin Das