Continuous time recurrent neural networks
(CTRNN) are systems of coupled ordinary differential equations
inspired by the structure of neural networks in the brain.
CTRNN are known to be universal dynamical approximators:
given a large enough system, the parameters of a CTRNN
can be tuned to produce output that is arbitrarily close ...
Continuous time recurrent neural networks
(CTRNN) are systems of coupled ordinary differential equations
inspired by the structure of neural networks in the brain.
CTRNN are known to be universal dynamical approximators:
given a large enough system, the parameters of a CTRNN
can be tuned to produce output that is arbitrarily close to
that of any other dynamical system. However, in practise, both
designing systems of CTRNN to have a certain output, and
the reverse—understanding the dynamics of a given system
of CTRNN—can be non-trivial. In this paper, we describe
a method for embedding any specified Turing machine in
its entirety into a CTRNN. As such, we describe in detail
a continuous-time dynamical system that performs arbitrary
discrete-state computations. We suggest that in acting as both
a continuous-time dynamical system and as a computer, the
study of such systems can help refine and advance the debate
concerning the Computational Hypothesis that cognition is
a form of computation and the Dynamical Hypothesis that
cognitive systems are dynamical systems.
