Konstantin Mischaikov
Department of Mathematics
Rutgers University
Tuesday, March 11, 2008
4:00PM in 127 Hayes-Healy
*Tea at 3:30 in 257 Hurley*
Building a Database for the Global Dynamics of Multiparameter Systems
Many applications involve nonlinear models, but specific parameters are unknown or not directly
measurable (this is particularly true for mathematical models in biology). Since the actual
dynamics can vary dramatically depending upon the parameters, it is iimportant to be able to
identify whether and at what parameter values specific dynamical behavior occurs. Further
complicating the issue is that nonlinear systems can both exhibit chaotic dynamics and be
structurally unstable for large sets of parameter values.
To deal with these issues we are developing techniques to construct databases of the dynamics
exhibited by specific multi-parameter systems. The basic idea is to identify and classify crude
dynamical structures using graph theoretic and computational topological and algebraic
topological techniques that are robust with respect to perturbations induced by numerical and
parametrical approximations.
Last Updated: Monday, February 25, 2008