Representation of first order dynamical systems using neural networks

The approximation of dynamical systems (DSs) using neural networks (NNs) is considered in this paper in a broader sense than the mere trajectory approximation for finite time. The object of this study is to try to determine the capabilities of NNs to reproduce structural properties of DSs in order to achieve approximation for all trajectories that remain in a closed region of the state space as t tends to infinity. This is a new approach to approximating DSs using NNs, which the authors call the representation of DSs rather than an approximation of trajectories. The problem so stated is under current research, and the preliminary results concerning first order dynamical systems are presented here