Abstract: Movement is fundamental to life as it is what allows us to interact with our environment. Daily tasks from walking to speaking are the result of voluntary muscle control. The brain center that controls voluntary motion is the motor cortex. We can model the motor cortex using Artificial Neural Networks. Although these models are computationally powerful, they are not typically analytically solvable. However, recently it has been shown that there are networks that can perform computations and which can be solved mathematically. In this presentation we explore these networks in the context of modelling the motor cortex, and how they can be used to capture motor trajectories of a six-muscle arm. We will then discuss the mathematical analysis done on a network which can model motor behaviour and which is solvable. This analysis involves concepts from Spectral Analysis and Linear Algebra.