DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Konstantin Mischaikow, Mathematics, Rutgers University

**Title: ***
Building a Database for the Global Dynamics of Multi-Parameter Systems
*

**Abstract:**
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 important 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.

**Time:** Friday, April 4, 2008, 1:30-2:30 p.m.

**Place:** Research I, Room 301

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491