TALK BY PETER BAXENDALE, OCTOBER 28, 2010
Sustained oscillations and density dependent Markov chains.
Peter Baxendale, University of Southern California
ABSTRACT: A number of recent papers have considered the phenomenon of sustained oscillations in density dependent Markov models of
processes in areas such as interacting populations, epidemics, and chemical kinetics. This talk will consist of three parts. One part
will describe a recent stochastic averaging result which explains the existence of sustained oscillations for a class of 2-dimensional
diffusion processes. A second part will survey the transition from the original density dependent Markov chain to a diffusion
approximation. (For mathematicians this is work of Kurtz from the 1970s; for physicists, chemists and biologists this is the Van Kampen
expansion). The last part will bring these ideas together to provide both qualitative and quantitative results on sustained
oscillations for density dependent Markov chains. This is joint work with Cindy Greenwood.