Dynamics of a stage-structured system with harvesting and discrete time delays

A two-dimensional single-species stage-structured model is proposed and analyzed to study the effect of intraguild predation with harvesting of the adult species. Time lags in reproduction and maturation of the organism are introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. It is found that there are stability switches for time delays, and Hopf bifurcations when time delays cross through some critical values. The stability and direction of the Hopf bifurcations are determined by applying the normal form method and the center manifold theory. Computer simulations have been carried out to illustrate various analytical results.