We study changes of coordinates that allow the embedding of ordinary differential equations
describing continuous-time recurrent neural networks into differential equations describing …

Recurrent Neural Networks (RNN) have been developed for a better understanding and
analysis of open dynamical systems. Still the question often arises if RNN are able to map …

Universality of Fully-Connected Recurrent Neural Networks 3 Page 1 Universality of Fully-Connected
Recurrent Neural Networks 3 Kenji Doya doya@crayfish.ucsd.edu Department of Biology …

Neural networks represent a class of functions for the efficient identification and forecasting
of dynamical systems. It has been shown that feedforward networks are able to approximate …

A ‘programming’ framework for recurrent neural networks | Nature Machine Intelligence Skip to
main content Thank you for visiting nature.com. You are using a browser version with limited …

In this paper, we prove that any finite time trajectory of a given n-dimensional dynamical
system can be approximately realized by the internal state of the output units of a continuous …

A Volterra-like polynomial representation is derived and its convergence discussed for two
neuronal models in which subthreshold inputs are integrated either without loss (integrate …

The stability analysis of dynamical neural network systems typically involves finding a
suitable Lyapunov function, as demonstrated in Hopfield's famous paper on content …

The main goal of this study is to elucidate the theoretical capability of the continuous time
recurrent neural network. In this paper, we show that the approximation capability of the …

A paper by Marmarelis and Zhao (1997) describes the use of what the authors call a"
separable Volterra network" for modeling high-order Volterra systems. This model is …