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Applied Math Colloquium

Friday, September 6th, 2013, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Unexpeccted Chaos in a Neural Model

Jonathan Rubin

Department of Mathematics, University of Pittsburgh

Abstract

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 under so-called balance conditions that yield cancellation of correlations. I will discuss a mechanism by which irregular, apparently chaotic activity emerges naturally in small inhibitory networks lacking such balance. I will present a one-dimensional map that captures this activity as well as analysis of how expansion, folding, and contraction emerge in a corresponding phase plane, as expected in chaotic dynamics.