Modeling Dynamical Systems – One Day Workshop

s of Talks Keynote Speeches Spatiotemporal dynamics in ecological systems Speaker: Alan Hastings Affiliation: Department of Environmental Science and Policy, University of California, Davis Abstract I will discuss some of the complexities involved in spatiotemporal dynamics in ecological systems, focusing on two aspects: the role of stochasticity in spatial spread and the dynamics of regime shifts. In discussing the role of stochasticity in spatial spread I will be emphasizing variance as uncovered in a laboratory system with flour beetles. This will naturally lead to discussions of regime shifts (sudden changes in dynamical behavior as in eutrophication) and the possibilities for detecting warning signs. Towards an understanding of chronic brain injury as a dynamical disease: a population-based model of thalamocortical circuits and EEG observables Speaker: Jonathan Victor Affiliation: Department of Neurology and Neuroscience, Cornell University Abstract Higher brain function depends on dynamic interactions of multiple cortical and thalamic populations. In patients with chronic disturbances of these functions due to brain injury, converging lines of evidence suggest that dynamical disturbances of these interactions play a crucial role in pathogenesis. However, assaying these interactions is challenging in healthy subjects, and even more so in severely impaired patients. With the goal of understanding how these interactions are manifest in the EEG, we have begun to build a model of thalamocortical populations. The basic building block is the thalamocortical module (cortex, relay nucleus, and reticular nucleus). We show that when two such modules are coupled via a shared reticular nucleus, multistable behavior emerges, with each mode characterized by a different pattern of corticocortical coherence. These observations support the role of the reticular thalamus in the organization of patterns of cortical interactions, and we present preliminary data that show how these features can be identified in the EEG. Authors: Jonathan D. Victor, Nicholas D. Schiff, Jonathan D. Drover