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The present paper deals with modification of the neural networks estimation method of the maximal Lyapunov exponent (MLE) for chaotic time series and development of this method for processing series with real world application. Namely, the necessity to use committees of neural networks for MLE calculation is strongly grounded. The method of estimating the Lyapunov exponent calculation error is elaborated. The technique of forecasted trajectories divergences averaging on the delayed pseudoattractor of time series is introduced. The separation of two important cases when MLE is zero and the case when it is small but positive is accomplished by making use of appropriate statistical tests. It is shown that even the modified method of neural networks committee MLE estimation can give positivity of MLE for stochastic series at relatively high statistical characteristics of the neural networks forecasts quality. Additional tests and researches for identification chaos in time series are required. The proposed approach is tested on the model chaotic and periodic time series as well on time series having real world application such as EEG signals and tensotremorogram signals.