Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-prey systems with discrete delays

The dynamics of delayed systems depend not only on the parameters describing the models but also on the time delays from the feedback. A delay system is absolutely stable if it is asymptotically stable for all values of the delays and conditionally stable if it is asymptotically stable for the delays in some intervals. In the latter case, the system could become unstable when the delays take some critical values and bifurcations may occur. We consider three classes of Kolmogorov-type predator-prey systems with discrete delays and study absolute stability, conditional stability and bifurcation of these systems from a global point of view on both the parameters and delays.