Stochastic dynamics of nonlinear waves in neuronal networks
Zachary Kilpatrick
Department of Mathematics, University of Houston
Date and time:
Thursday, November 20, 2014 - 11:30am
Location:
ECCR 257
Abstract:
Neural fields are nonlinear integrodifferential equations whose integral term describes the strength of connections between neurons in a large network. Neural fields have been used to model activity waves and oscillations in the brain underlying epileptic seizures, short term memory, and visual hallucinations. Typical analyses of neural fields consider network architectures that are spatially homogeneous. In this talk, we show that more realistic network architectures can be utilized to improve network performance of cognitive tasks. We model the persistent neural activity underlying short term memory as a stationary pulse (bump), analyzing its effective dynamics using asymptotic methods. Introducing spatial heterogeneity into network architecture establishes a multistable potential landscape, slowing the rate at which noise causes the bump to diffuse in space. Ultimately, this improves the accuracy with which the network encodes memories. This work is extended to analyze networks with multiple layers, delays, and negative feedback. We also show that similar approaches can be used to analyze wave propagation in stochastic neural fields.