Critical delay for overshooting in planned arm movements with delayed feedback.

The Vector Integration To Endpoint (VITE) circuit describes a real time neural network model which simulates behavioral and neurobiological properties of planned arm movements by the interaction of two populations of neurons. This model is generalized to include delay between the interacting populations, which is found to have a detrimental effect on movement accuracy. Conditions are given on the model parameters for accurate movement and target overshoot, where we show that there exists a non-zero critical value of the delay which the circuit can support while maintaining accurate movement. This critical delay depends on the movement speed, and becomes arbitrarily large for sufficiently slow movement. Thus neurobiological or artificial systems modelled by the VITE sensory-motor loop can tolerate an arbitrarily large delay if the movement speed is sufficiently slow.