How we perceive the world is governed both by the sensory inputs with which we are constantly bombarded, by ongoing activity in the brain, and by our previous experience. This activity as well as the natural wiring of the nervous system shapes the spontaneous behavior of our brains and this spontaneous activity strongly modulates the sensory inputs. In this project, computational and mathematical models of neurons (the cells that make up the brain) are used to understand what kinds of spontaneous behavior are possible, how this depends on the wiring and how this activity interacts with sensory inputs. The ongoing and evoked behavior is carefully controlled by a balance of positive (excitatory) and negative (inhibitory) influences. The loss of this balance can disrupt normal behavior and lead to diseases such as epilepsy and schizophrenia. Mathematical models of the nervous system provide a way to test hypotheses put forth by experimenalists and to also suggest new experiments based on the predictions of these models.
Ongoing activity in the nervous system and how it impacts sensory and other inputs is the subject of much recent experimental activity. In particular, it is clear that the intrinsic interactions between neuronal circuits in absence of inputs can have a strong impact on how the system responds to incoming stimuli even at the large scale cognitive level. Thus, nonlinear dynamics methods will be applied to problems in theoretical neuroscience dealing with this question. Various forms of spatiotemporal activity are observed in experiments which include spatially localized activity, oscillations, and propagating waves. Perturbation and numerical methods will be used to analyze the dynamics of these patterns when subjected to various stimuli such as flickering light, localized or moving stimuli, and spatially periodic patterns. Uniform flickering stimuli lead to the perception of moving geometric patterns and these can be explained by the analysis of mean field models of visual cortex. In collaboration with an experimental group we will use the modeling to make predictions about how this percept is altered as parameters of the flicker vary. Related to this is the appearance of flicker when presented with high contrast spatially periodic patterns. Stability of the steady periodic state will be studied in order to see if the appearance of oscillations is the result of a Hopf bifurcation. This effect may also offer an explanation for why some images (such as op art) can induce visual discomfort. The existence an properties of traveling waves in nonlocally connected networks will also be studied in this project.
