Modeling of continuous time dynamical systems with input by recurrent neural networks

This paper proves that any finite time trajectory of a given n-dimensional dynamical continuous system with input can be approximated by the internal state of the output units of a continuous time recurrent neural network (RNN). The proof is based on the idea of embedding the n-dimensional dynamical system into a higher dimensional one. As a result, we are able to confirm that any continuous dynamical system can be modeled by an RNN.