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Nonlinear Dynamics

, Volume 79, Issue 2, pp 1049–1059 | Cite as

A wavelet-based approach for stability analysis of periodic delay-differential systems with discrete delay

  • Ye Ding
  • LiMin Zhu
  • Han Ding
Original Paper

Abstract

This paper presents a semi-analytical wavelet-based approach for stability analysis of time-periodic delay-differential equations (DDEs) with a single discrete time delay. By using the autocorrelation functions of compactly supported Daubechies scaling functions, the DDE is discretized to a set of algebraic equations, employing the wavelet collocation method. The state transition matrix over a single period is constructed to determine the stability based on Floquet theory. Stability charts for the one-degree-of-freedom milling model and time-delayed Mathieu equation are obtained, illustrating both the efficiency and accuracy of the proposed approach.

Keywords

Delay-differential equation Stability Daubechies scaling function Interpolating wavelet Floquet theory 

Notes

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 51305263 and 51325502). The last author was supported by the National Key Basic Research Program (Grant No. 2011CB706804).

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.State Key Laboratory of Mechanical System and Vibration, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina
  2. 2.State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhanChina

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