A Yu Pogromsky et al 2003 Nonlinearity 16 1597 doi:10.1088/0951-7715/16/5/303
A Yu Pogromsky1, G Santoboni2 and H Nijmeijer1
Show affiliationsRecommended by G Moriss
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.
34D45 Attractors (See also 37C70, 37D45)
34D08 Characteristic and Lyapunov exponents
34D30 Structural stability and analogous concepts (See also 37C20)
Issue 5 (September 2003)
Received 24 February 2003, in final form 27 May 2003
Published 20 June 2003
A Yu Pogromsky et al 2003 Nonlinearity 16 1597
Vasilii A Iskovskikh et al 1988 Russ. Math. Surv. 43 201
Chi-Hsuan Lin et al 2006 Physiol. Meas. 27 119
Anton Kapustin and Mikhail Tikhonov JHEP11(2009)006
Hao Xing et al 2006 Meas. Sci. Technol. 17 510
I Alexandrou et al 2003 Nanotechnology 14 913
R Santra et al 2007 J. Phys.: Conf. Ser. 88 012052
Gilad Gour and Robert W Spekkens 2008 New J. Phys. 10 033023
Jacek Pawełczyk and Rafał R. Suszek JHEP04(2006)009
Peter G Kaup et al 1996 Inverse Problems 12 279