Multilayer feedforward networks can learn strange attractors

• Published in: IJCNN-91-Seattle International Joint Conference on Neural Networks Vol. ii; pp. 139 - 144 vol.2
• Main Author: Welstead, S.T.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 1991
• Subjects: Chaos; Computer networks; Displays; Feedforward neural networks; Multi-layer neural network; Neural networks; Nonhomogeneous media; Shadow mapping; Time series analysis
• ISBN: 0780301641; 9780780301641
• DOI: 10.1109/IJCNN.1991.155327

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.< >