Network stability within visual cortex: A Lyapunov function approach

The cerebral cortex is a brain region that is implicated in complex behaviors. Understanding the dynamics of neurons in areas of the cerebral cortex is, thus, an important goal in neuroscience. Methods for recording the activity of populations of neurons in cortical areas are now becoming available, but there are few analytic methods available to analyze such data. This paper introduces a simple dynamical systems model based on a family of linear, non-autonomous differential equations that can be used to model such data. It also introduces a simple method of constructing Lyapunov functions for this family of equations.