DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** >Juan Sabuco, Universidad Rey Juan Carlos, Madrid, Spain

**Title: ***
Partial Control of Chaotic Systems
*

**Abstract:**
The partial control technique allows one to keep the trajectories of a
dynamical system inside a region where there is a chaotic saddle and
from which nearly all the trajectories diverge. Its main advantage is
that this goal is achieved even if the corrections applied to the
trajectories are smaller than the action of environmental noise on the
dynamics, a counterintuitive result that is obtained by using certain
safe sets. A fundamental step towards this goal is to compute those
sets, that so far could be only found in certain situations. Here we
provide a general algorithm to compute those safe sets. The algorithm
is able to compute the safe sets by simply knowing the region in phase
space, the noise value and the desired maximum control. We call it
Iterative Sculpting Algorithm, as an analogy to removing material as
in sculpting a statue, since this is what happens to obtain the safe
sets. As an example, we show the application of the algorithm to two
paradigmatic nonlinear dynamical systems: the Hénon map and the
Duffing oscillator.

**Time:** Friday, Dec. 9, 2011, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

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