Title :
Applications of a new ultimate bound on the trajectories of the Lorenz system to synchronization and estimation of the Hausdorff dimension
Author :
Pogromsky, A. ; Santoboni, G. ; Nijmeijer, H.
Author_Institution :
Dept. of Mech. Eng., Eindhoven Univ. of Technol., Netherlands
Abstract :
In this paper a new bound on the trajectories of the Lorenz system is derived. This result is useful to show that the transverse stability of the origin in two Lorenz systems coupled in a drive-response manner is a necessary and sufficient condition for global asymptotic synchrony of the two systems. It also enables to simplify the derivation of an upper bound of the Hausdorff dimension of the Lorenz attractor.
Keywords :
asymptotic stability; synchronisation; Hausdorff dimension estimation; Hausdorff dimension synchronization; Hausdorff dimension upper bound; Lorenz attractor; Lorenz system trajectory; asymptotic synchrony; necessary condition; sufficient condition; transverse stability; Asymptotic stability; Chaos; Petroleum; Sufficient conditions;
Conference_Titel :
Physics and Control, 2003. Proceedings. 2003 International Conference
Print_ISBN :
0-7803-7939-X
DOI :
10.1109/PHYCON.2003.1236906
