Incompressible viscous fluid flows in a thin spherical shell Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional Navier-Stokes equations on a sphere. The stationary flow

S 1.2 DONALD CAMPBELL University of Waterloo The Sigma-Delta Modulator as a Chaotic Nonlinear Dynamical System Sigma-Delta modulators (or noise shapers, as they are also called) are extensively used for analogue-to-digital and digital-to-analogue data conversion (signal processing). Their dynamical behaviour can appear chaotic. I will explore this behaviour from the point of view of nonlinear dynamical systems analysis. To begin, the difference equation model of the sigma-delta modulator is introduced, and some basic results for bounded stability are obtained. The model is cast formally as a discrete dynamical system, and important continuity results allowing for a linear analysis are established. Drawing on this, I conduct a theoretical study of conditions for chaos or nonchaos using an adaptation of Devaneys definition of chaos. This study is extended to the dithered system, in the context of allowing stochatic aspects in the model. I then introduce a stochastic formulation of the long-run dynamics, which is applied to give conditions for uniformly distributed error behaviour conditions under which important consequences arise when dither is used to control the error statistics. OLIVER DIAZ-ESPINOSA McMaster University Small random perturbations of critical dynamical systems We consider one dmensional maps that admit a renormalization group analysis. Under small random perturbations of such maps, we show that there is a universal scaling limit which is a Gaussian. RALUCA EFTIMIE University of Alberta Modeling complex spatial animal group patterns: the role of different communication mechanisms I will present newly discovered spatial group patterns that emerge in a one-dimensional hyperbolic model for animal group formation and movement. The patterns are the result of the assumptions that the interactions governing movement depend not only on distance between conspecifics, but also on how individuals receive information about their neighbors, and the amount of information received. Some of these patterns are classical, such as stationary pulses, traveling waves, or traveling trains. However, most of the patterns are new. We call these patterns zigzag pulses, semi-zigzag pulses, traveling breathers and feathers.