Geometry of V-functions and the 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.

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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

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Recent Advances in Liapunov Stability Theory

SIAM Review ◽

10.1137/1006001 ◽

1964 ◽

Vol 6 (1) ◽

pp. 1-11 ◽

Cited By ~ 17

Author(s):

J. P. LaSalle

Keyword(s):

Stability Theory ◽

Liapunov Stability ◽

Recent Advances

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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.

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