Almost surely non-linear solutions of stochastic linear delay equations

1985 ◽  
pp. 270-275
Author(s):  
S. E. A. Mohammed
Keyword(s):  
Delay Equations ◽  
Linear Delay ◽  
Non Linear

scholarly journals Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
T. S. Doan ◽  
S. Siegmund
Keyword(s):  
Finite Time ◽  
Delay Equations ◽  
Volterra System ◽  
Time Intervals ◽  
Linear Delay ◽  
Diagonally Dominant ◽  
Coupling Terms

We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.

The Modulus Semigroup for Linear Delay Equations

Positivity ◽  
2004 ◽  
Vol 8 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Said Boulite ◽  
Lahcen Maniar ◽  
Abdelaziz Rhandi ◽  
Jürgen Voigt
Keyword(s):  
Delay Equations ◽  
Linear Delay
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