Permitted and Forbidden Sets in Symmetric Threshold-Linear Networks

Ascribing computational principles to neural feedback circuits is an important problem in theoretical neuroscience. We study symmetric threshold-linear networks and derive stability results that go beyond the insights that can be gained from Lyapunov theory or energy functions. By applying linear analysis to subnetworks composed of coactive neurons, we determine the stability of potential steady states. We find that stability depends on two types of eigenmodes. One type determines global stability and the other type determines whether or not multistability is possible.