Abstract
This paper investigates positivity and asymptotic stability for a class of timescale-type differential–difference equation with time-varying delay. When the delay is bounded, a necessary and sufficient condition is obtained based on timescale theory and comparison principle. While for the case of unbounded delay, a sufficient criterion is acquired. Further, for the corresponding continuous-time system with unbounded delay, a necessary and sufficient condition is secured under an extra constraint. This work relaxes a previous assumption on the unbounded time-varying delay and also generalizes and deepens some existing results.
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