A neural' network applied to tlie calculation of lyapunov exponents1
研究了用反向传播神经网络间接估计混沌吸引子最大李雅普诺夫指数的方法，解决了直接法（Wolf算法）在中等规模数据集上失效的问题，并通过多个例子验证了该方法能恢复理论值。
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.