Control in chaotic saddles

Jacobo Aguirre and A. F. Sanjuán

Universidad Rey Juan Carlos Madrid, Spain

Francesco d'Ovidio and Erik Mosekilde

Department of Physics, Technical University of Denmark, 2800 Kongens Lyngby, Denmark.

Abstract: We study the possibility of using control for trapping the dynamics of a system inside a chaotic saddle in presence of noise. In chaos control, typically unstable orbits embedded in a chaotic set are targetted. Here instead we present a control technique that exploits the non-attracting nature of a chaotic saddle targetting preimages of the escaping regions. This technique is able to keep the system inside the chaotic saddle indefinitely and is extremely robust against noise: for the tent map, the ratio between maximum noise and maximum control is up to two. Moreover, all the information that is needed can be obtained by simple time series analysis, allowing to apply such technique to real system.