A neural' network applied to tlie calculation of lyapunov exponents

Chaotic deterministics systems are characterised by the instability of orbits on an attractor. The largest Lyapunov exponent measures on average the exponential growth rate of small deviations along an orbit and gives as such an indication whether or not the dynamic generating process is unstable. The direct method for calculation of the Lyapunov exponent, based on finite differences as formulated by the so-called Wolf-algorithm,fails on medium sized data sets. Alternatively, one can use a neural network with backpropagation to estimate a data generating function. This so-calletl indirect method enables us to recover the theoretical value of the largest Lyapunov exponent in several examples.