The joint impacts of maturation delay and digestion delay on the dynamics of a predator⁃prey model

The dynamics of a predator⁃prey model with maturation and digestion delays were studied. The characteristic equation with delay-dependent parameters was first analyzed using the geometric method. Accordingly， the Hopf bifurcation curve and unstable region on the two-delay plane were obtained. The center manifold and normal form theory were then applied to deduce the criteria for judging the bifurcation direction and the stability of the bifurcation periodic orbit. Combined with numerical examples， it was found that， as the digestion delay increases， the model would lose its stability. In contrast， as the maturation lag increases， the model would tend to be stable after finite stability switches.