Graphs, neural networks, and emergent dynamics in the brain
Carina Curto, Pennsylvania State University
Many networks in the brain display internally-generated patterns of activity -- that is, they exhibit emergent dynamics that are shaped by intrinsic properties of the network rather than inherited from an external input. While a common feature of these networks is an abundance of inhibition, the role of network connectivity in pattern generation remains unclear. In this talk I will introduce Combinatorial Threshold-Linear Networks (CTLNs), which are simple "toy models" of recurrent networks consisting of threshold-linear neurons with effectively inhibitory interactions. The dynamics of CTLNs are controlled solely by the structure of an underlying directed graph. By varying the graph, we observe a rich variety of nonlinear dynamics including: multistability, neuronal sequences, and complex rhythms. These patterns are reminiscent of population activity in cortex, hippocampus, and central pattern generators for locomotion. I will present some new theorems about CTLNs, and explain how they allow us to predict features of the dynamics by examining properties of the underlying graph.