Professor, Department of Mathematics
University of Pittsburgh
December 8, 2015
Irregular neural activity: how to achieve it and how to restore it
Baseline activity in many brain regions is believed to be irregular, with little correlation in firing times of different neurons. Indeed, excessive regularity has been associated with disorders such as Parkinson's disease. Mathematically, neuronal irregularity has been represented as an asynchronous state that can be stable, in a large-network limit, under so-called input balance conditions that may yield cancellation of correlations. I will discuss a mechanism by which irregular, apparently chaotic activity emerges naturally in small networks lacking such balance, including purely inhibitory networks. The result can be observed in a two-neuron network, where a one-dimensional map captures this activity and where expansion, folding, and contraction, as expected in chaotic dynamics, can be analyzed. In conditions where pathology is associated with excessive regularity, restoring irregularity may be therapeutic, and thus I will also briefly turn to a mechanism by which deep brain stimulation for parkinsonism may desynchronize neural activity.