Konstantin Mischaikow - Rutgers University
Date/Time/Location
Thursday, March 5th, 2:00pm; Hill 705
Title
"An approach to solving dx/dt = ?"
The life sciences provide archetypical examples of nonlinear systems for which an accurate understanding dynamics is essential, but for which models derived from first principles are not available. This implies that an analytic expression of a nonlinearity is typically chosen based on heuristics or simplicity of evaluation. As a consequence parameters do not have an intrinsic physical basis, but bifurcation theory tells us that in general the invariant sets of a dynamical system are parameter dependent. Furthermore experimental measurements of variables tend to be quantified on log scales. This is not a setting for which the classical theory of dynamical systems was designed to address. With these challenges in mind I will outline an approach to dynamics based on order theory and algebraic topology that allows us to consider large classes of differential equations over large regions of parameter space and derive rigorous results. I will use gene regulatory networks to provide a concrete example of how this approach can be applied.