UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Friday (09/03/2004) at 2:00pm in 304 Pickard Hall

Speaker: Professor Kresimir Josic, Department of Mathematics, University of Houston

"Synchrony in networks of systems with complex behavior"

Abstract: In the first part of the talk I will discuss the relation between the theory of normal forms and some of these classical perturbation techniques and introduce a method based on normal form analysis which provides an algorithmic way of obtaining rigorously justifiable approximations to solutions of certain ODEs on long timescales. I will illustrate the method by analyzing synchrony in a network of different types of weakly nonlinear oscillators. In the second part I will address the problem of phase synchrony in complex system, and present examples of this phenomenon in neuroscience. A mathematical theory explaining the phenomenon will be discussed. Although, in some respects, the results are similar to those obtained for noisy systems, there are certain surprising differences.