SS15 AIMS 2016 Meeting, Orlando, Florida, USA

Title:  Special Session on Monotone Dynamical Systems and Applications
Name: Affiliation: Country: Email Address:
Hal L. Smith
School of Mathematical and Statistical Sciences Arizona State University Tempe, AZ, U.S.
Janusz Mierczy`nski
Department of Mathematics Wroclaw University of Technology Wroclaw, Poland
The theory of monotone dynamical systems grew out of the much earlier and well-developed monotone methods and comparison theory largely through the work of M.W. Hirsch and H. Matano in the 1980`s. Essentially, the theory focuses on the implications of order-preservation of the (semi-) flow map on the asymptotic behavior of solutions. Typically, the asymptotic behavior of order-preserving dynamical systems is much simpler than for generic systems. Applications of the theory to systems of ordinary differential equations, delay differential equations, parabolic partial differential equations, and to the discrete-time dynamics generated by monotone maps and systems of difference equations have grown rapidly. Mathematical models in biology and chemical reaction dynamics are a rich source of applications because state variables are often intrinsically nonnegative and therefore the requirement that the dynamics be order-preserving is less restrictive. Recently, the theory has been extended to a control theory setting that includes system inputs and outputs and to random dynamical systems as well to stochastic games. New applications have arisen by identifying novel order relations preserved by special classes of dynamical systems. This special session will focus on these recent developments in both theory and applications.
List of approved abstract