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.
T. S. Doan. S. Siegmund. "Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays." Abstr. Appl. Anal. 2012 (SI09) 1 - 10, 2012. https://doi.org/10.1155/2012/210156