Monotone Systems and the Stability of Biological Systems

German Enciso
Department of Mathematics and Statistics, Arizona State University

(November 10, 2005 10:30 AM - 11:30 AM)

Monotone Systems and the Stability of Biological Systems

Abstract

Determining the long-time behavior of large dynamical systems has proved to be a remarkably difficult problem. And yet the robustness and stability of molecular networks in biology seems to indicate a certain underlying structure that doesn't change under (some) small changes in the topology or the parameter values. Using the theory of monotone systems, we have tried to underline some of the relevant stability features of certain potentially high-dimensional systems. In this talk, I give sufficient qualitative and quantitative conditions for global attractivity and multistability, even for systems that are not monotone themselves, with applications to delay differential equations arising in molecular biology.