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

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