2016年10月
ON PARAMETER DEPENDENCE OF EXPONENTIAL STABILITY OF EQUILIBRIUM SOLUTIONS IN DIFFERENTIAL EQUATIONS WITH A SINGLE CONSTANT DELAY
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- 巻
- 36
- 号
- 10
- 開始ページ
- 5657
- 終了ページ
- 5679
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.3934/dcds.2016048
- 出版者・発行元
- AMER INST MATHEMATICAL SCIENCES-AIMS
A transcendental equation lambda + alpha - beta e (lambda tau) = 0 with complex coefficients is investigated. This equation can be obtained from the characteristic equation of a linear differential equation with a single constant delay. It is known that the set of roots of this equation can be expressed by the Lambert W function. We analyze the condition on parameters for which all the roots have negative real parts by using the "graph-like" expression of the W function. We apply the obtained results to the stabilization of an unstable equilibrium solution by the delayed feedback control and the stability condition of the synchronous state in oscillator networks.
- リンク情報
- ID情報
-
- DOI : 10.3934/dcds.2016048
- ISSN : 1078-0947
- eISSN : 1553-5231
- Web of Science ID : WOS:000385220600022