Recent Advances in Liapunov Stability Theory

AbstractCriteria for guaranteeing the existence, uniqueness and asymptotic stability (in the sense of Liapunov) of periodic solutions of a forced Liénard-type equation under certain assumptions are presented. These criteria are obtained by application of the Manásevich–Mawhin continuation theorem, Floquet theory, Liapunov stability theory and some analysis techniques. An example is provided to demonstrate the applicability of our results.

Maneuver and vibration control of nonlinear hybrid coordinate systems using Liapunov stability theory

10.2514/6.1992-4458 ◽

1992 ◽

Cited By ~ 1

Author(s):

JOHN JUNKINS ◽

HYOCHOONG BANG

Keyword(s):

Vibration Control ◽

Stability Theory ◽

Coordinate Systems ◽

Liapunov Stability ◽

Nonlinear Hybrid

Some recent Advances in Plasma Stability Theory

Physik Journal ◽

10.1002/phbl.19790351212 ◽

1979 ◽

Vol 35 (12) ◽

pp. 611-616 ◽

Cited By ~ 3

Author(s):

J. B. Taylor

Keyword(s):

Stability Theory ◽

Plasma Stability ◽

Recent Advances

A NEW SYNCHRONIZATION PRINCIPLE AND APPLICATION TO CHUA'S CIRCUITS

International Journal of Bifurcation and Chaos ◽

10.1142/s021812740200470x ◽

2002 ◽

Vol 12 (04) ◽

pp. 815-818 ◽

Cited By ~ 7

Author(s):

YONGAI ZHENG ◽

ZENGRONG LIU ◽

JIN ZHOU

Keyword(s):

Stability Theory ◽

Coupling Constants ◽

Coupling Constant ◽

Chaotic Oscillators ◽

Large Coupling ◽

Liapunov Stability ◽

Large Coupling Constant ◽

Hurwitz Theorem

In the paper we propose a new synchronization principle. To guarantee synchronization between coupled chaotic oscillators, proper coupling constants are selected by the Liapunov stability theory and Hurwitz Theorem. As an example and application, we prove the conjecture [Wu & Chua, 1994] that synchronization between two chaotic Chua's circuits can be achieved by using the second state as feedback variable for sufficiently large coupling constant.

Geometry of V-functions and the Liapunov stability theory

Nonlinear Analysis ◽

10.1016/0362-546x(87)90097-6 ◽

1987 ◽

Vol 11 (2) ◽

pp. 183-197 ◽

Cited By ~ 2

Author(s):

E.A. Galperin ◽

J.M. Skowronski

Keyword(s):

Stability Theory ◽

Liapunov Stability

Recent Advances in High Dispersion Spectroscopy of Globular Cluster Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900035610 ◽

1988 ◽

Vol 132 ◽

pp. 525-530

Author(s):

Raffaele G. Gratton

Keyword(s):

Globular Cluster ◽

Globular Clusters ◽

High Dispersion ◽

Photographic Material ◽

Recent Advances ◽

Metal Abundances ◽

Ccd Detectors ◽

Major Progress

The use CCD detectors has allowed a major progress in abundance derivations for globular cluster stars in the last years. Abundances deduced from high dispersion spectra now correlates well with other abundance indicators. I discuss some problems concerning the derivation of accurate metal abundances for globular clusters using high dispersion spectra from both the old photographic and the most recent CCD data. The discrepant low abundances found by Cohen (1980), from photographic material for M71 giants, are found to be due to the use of too high microturbulences.