The behaviour of non-linear dynamic systems is studied. Through numerical experiments the coefficients of the non-linear differential equations are identified. In this paper, the authors present an investigation of the modelling and prediction abilities of a traditional Recurrent Neural Network (RNN) and a Long Short-Term Memory (LSTM) RNN, when the input signal has a chaotic nature. The effectiveness of both networks in modelling the Lorenz System is studied. And a comparison of their respective one-step ahead predictions is made.