Multilayer feedforward networks can learn strange attractors

It is shown that not only can multilayer feedforward networks (MFNs) emulate observed nonlinear processes, but, when allowed to operate as dynamical systems, they perform in a complex dynamical manner of their own. In particular, when such a network is trained on data generated by a dynamical system that is known to be chaotic, the trained network, operating as a dynamical system, displays a strange attractor of its own that is similar to the strange attractor of the original system. Analysis involving shadowing results shows that a neural network can be expected to learn a strange attractor. Evidence of the chaotic nature of the network strange attractor is provided numerically by the computation of a positive Lyapunov exponent. An application of this idea is that MFNs can be used to reveal the strange attractors associated with chaotic experimental time series, and to provide a simple means for estimating their Lyapunov exponents