Chaotic dynamics of supervised neural network

Abstract

It is important to study the neural network (NN) when it falls into chaos, because brain dynamics involve chaos. In this paper, the several chaotic behaviors of supervised neural networks using Hurst Exponent (H), fractal dimension (FD) and bifurcation diagram are studied. The update rule for NN trained with back-propagation (BP) algorithm absorbs the function of the form x(1-x) which is responsible for exhibiting chaos in the output of the NN at increased learning rate. The H is computed with the time series obtained from the output of NN. One can comment on the classification of the network from the values of Hs. The chaotic dynamics for two bit parity, cancer, and diabetes problems are examined. The result is validated with the help of bifurcation diagram. It is found that the values of H are repositioned marginally depending on the size of NN. The effect of the size of NN on chaos is also investigated.