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, and to simplify the derivation of the upper bound to the Hausdorff dimension of the Lorenz attractor. [References: 9]
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