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

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 domina...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2012-01, Vol.2012 (2012), p.1592-1601
Main Authors: Doan, T. S., Siegmund, Stefan
Format: Article
Language:English
Subjects:
Delay
Dynamical systems
Evolution
Intervals
Joining
Lotka-Volterra equations
Mathematical analysis
Nonlinearity
Ordinary differential equations
Power plants
Predator-prey simulation
Probability
Studies
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2012/210156