Applications of a new ultimate bound on the trajectories of the Lorenz system to synchronization and estimation of the Hausdorff dimension

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...

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Bibliographic Details
Main Authors: Pogromsky, A., Santoboni, G., Nijmeijer, H.
Format: Conference Proceeding
Language:English
Subjects:
Asymptotic stability
Chaos
Petroleum
Sufficient conditions
Online Access:Request full text
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Summary: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.
DOI:10.1109/PHYCON.2003.1236906