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Nonlinear Dynamics

, Volume 73, Issue 3, pp 1245–1251 | Cite as

Stability to vector Liénard equation with constant deviating argument

  • Cemil Tunç
Original Paper

Abstract

In this paper, we consider the vector Liénard equation with the constant deviating argument, τ>0,
$$X''(t) + F\bigl(X(t),X'(t) \bigr)X'(t) + H\bigl(X(t - \tau)\bigr) = P(t) $$
in two cases: (i) P(.)≡0, (ii) P(.)≠0. Based on the Lyapunov–Krasovskii functional approach, the asymptotic stability of the zero solution and the boundedness of all solutions are discussed for these cases. We give an example to illustrate the theoretical analysis made in this work and to show the effectiveness of the method utilized here.

Keywords

Vector Liénard equation Stability Constant deviating argument 

Notes

Acknowledgement

The author of this paper would like to expresses his sincere appreciation to the anonymous referees for their valuable comments and suggestions which have led to an improvement in the presentation of the paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesYüzüncü Yıl UniversityVanTurkey

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