[1] Ji Guojun,. Quadratic integrability of solutionsbased on a class of delayed systems [J]. Journal of Southeast University (English Edition), 2007, 23 (4): 630-638. [doi:10.3969/j.issn.1003-7985.2007.04.030]

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Quadratic integrability of solutionsbased on a class of delayed systems()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

23

Issue:

2007 4

Page:

630-638

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2007-12-30

Info

Title:

Quadratic integrability of solutionsbased on a class of delayed systems

Author(s):

Ji Guojun

School of Management, Xiamen University, Xiamen 361005, China

Keywords:

nonlinear delayed system;  quadratic integrability;  periodic solution;  oscillatory solution;  over-voltage

PACS:

O175.27;TM81

DOI:

10.3969/j.issn.1003-7985.2007.04.030

Abstract:

Some properties such as oscillation, stability, existence of periodic solutions and quadratic integrability of solutions based on a class of second order nonlinear delayed systems are analyzed by using the V-function, the Lyapunov functional or the Beuman-Bihari inequality, and some sufficient conditions based on those properties are given.Finally, the conclusions are applied to over-voltage models based on three-phase nonsynchronous closing of switches appearing in the power systems, the results in accord with the background physical meaning are obtained.And all the conditions of the conclusions are easy to validate, so the conclusions have definite theoretical meaning and are easy to apply in practice.

References:

[1] Ji Guojun.Asymptotic behavior of the nonlinear neutral differential equations [J].Journal of Xiamen University, 2005, 44(2):159-163.(in Chinese)
[2] Ji Guojun, Wang Zhengxian, Lai Dingwen.The periodic solutions existence of the overvoltage models in power systems [J].Acta Mathematica Scientia, 1996, 16(1):99-104.
[3] Ji Guojun, Wang Zhengxian.The functional differential equations appeared in the overvoltage [C]//Proceedings of International Functional Differential Equations.Beijing:Publishing House of Electronics Industry, 1994:123-128.
[4] Ji Guojun, Song Wenzhong.Study of the nonsynchronous closing overvoltage control models appeared in power systems [J].Journal Acta Mathematicae Applicatae, 1999, 22(4):46-53.(in Chinese)
[5] Li Yuesheng.Eigenfunction expansions associated with second-order differential equations [J].Journal of Math, 1962, 12:32-39.(in Chinese)
[6] Burton T A.Stability and periodic solution of ordinary and functional equations [M].Academic Press, 1985.
[7] Ladde G S, Lakshinikantham V, Zhang B G.Oscillation theory of differential equations with deviating arguments [M].Berlin:Springer-Verlag, 1991.
[8] Ji Guojun.Robust control for a class of chaotic nonlinear time-delay systems [J].Impulsive Dynamical Systems and Applications, 2006, 3:386-391.

Memo

Memo:

Biography: Ji Guojun(1964—), male, doctor, professor, jiking@xmu.edu.cn.

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