Abstract
A transcendental equation λ + α - βe-λτ = 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.
Original language | English |
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Pages (from-to) | 5657-5679 |
Number of pages | 23 |
Journal | Discrete and Continuous Dynamical Systems- Series A |
Volume | 36 |
Issue number | 10 |
DOIs | |
Publication status | Published - 2016 Oct |
Externally published | Yes |
Keywords
- Delay differential equations
- Equilibrium solutions
- Exponential stability
- Single constant delay
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics