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Approximation of dynamical systems by continuous time recurrent neural networks

✍ Scribed by Ken-ichi Funahashi; Yuichi Nakamura

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
431 KB
Volume
6
Category
Article
ISSN
0893-6080

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✦ Synopsis

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 time recurrent neural network with n output units, some hidden units, and an appropriate initial condition. The essential idea ofthe proof is to embed the n-dimensional dynamical system into a higher dimensional one which defines a recurrent neural network. As a corollary, we also show that any continuous curve can be approximated by the output of a recurrent neural network.

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