Stability Criteria for a System Involving Two Time Delays

A system of two autonomous ordinary differential equations with two discrete time delays is considered, with a view to determining the stability of equilibria. Using the Nyquist criterion on the characteristic equation, estimates on the length of delays are given for which a system which is stable in the absence of delays remains stable. Conditions are also derived for there to be no change in stability, even for unbounded delays. The above-mentioned criteria are applied to a system modeling competitive interacting populations, and to a predator-prey system.