Mathematical Biology Seminar Andrea Barreiro, University of Illinois at Urbana-Champaign Tuesday February 4, 2008 3:05pm in LCB 219 "Bifurcation Theory for a Model of the Oculomotor Neural Integrator" Abstract: In order to control the movement of the eyes, the brain must convert sensory signals proportional to desired eye velocity into eye position commands. The neural network that accomplishes this is the oculomotor neural integrator. This network produces integration through positive feedback and maintains a time constant of about 20 seconds in humans. In order to ensure that the integrator produces effective eye position commands under changing circumstances, it is regulated by the cerebellum. The cerebellar control mechanism is capable of independent adjustment of time constant and gain. We analyze neural network models of the coupled integrator-cerebellar system. Our analysis, which uses ideas from the perturbation theory of operators and classical differential geometry, shows that, in order to function normally, the system must operate in a narrow region where small perturbations can push it into regions of instability or oscillations. Our model will also simulate a class of eye movement disorders known as "congenital nystagmus". Both normal and abnormal behavior depend crucially on the non-normality of the system.