On characteristic roots and stability charts of delay differential equations

2011 ◽  
Vol 22 (8) ◽  
pp. 892-917 ◽  
Author(s):  
D. Breda
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Characteristic Roots ◽  
Delay Differential

Estimation of Time-Delays Using the Characteristic Roots of Delay Differential Equations

2011 ◽  
Author(s):  
Sun Yi ◽  
Sangseok Yu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Time Delays ◽  
Delay Systems ◽  
Lambert W Function ◽  
Short Paper ◽  
Characteristic Roots ◽  
General Systems ◽  
Delay Differential ◽  
Estimation Of Time

In this short paper, the preliminary result of a new method for estimation of time-delays of time-delay systems is presented. The presented method makes use of the Lambert W function, and is for scalar first-order delay differential equations (DDEs). Possible extension to general systems of DDEs and application to physical systems are also discussed.

Homotopy continuation for characteristic roots of delay differential equations using the Lambert W function

2017 ◽  
Vol 24 (17) ◽  
pp. 3944-3951 ◽  
Author(s):  
Samukham Surya ◽  
C. P. Vyasarayani ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Differential Equations ◽  
Characteristic Equation ◽  
Delay Differential Equations ◽  
Continuation Method ◽  
Lambert W Function ◽  
Homotopy Continuation ◽  
Multiple Delays ◽  
Homotopy Continuation Method ◽  
Characteristic Roots ◽  
Delay Differential

In this work, we develop a homotopy continuation method to find the characteristic roots of delay differential equations with multiple delays. We introduce a homotopy parameter μ into the characteristic equation in such a way that for μ = 0 this equation contains only one exponential term (corresponding to the largest delay) and for μ = 1 the original characteristic equation is recovered. For μ = 0, all the characteristic roots can be expressed in terms of the Lambert W function. Pseudo-arclength continuation is then used to trace the roots as a function of μ. We demonstrate the method on several test cases. Cases where it may fail are also discussed.

Sign in / Sign up

Export Citation Format

Share Document