Dynamics of asymmetric intraguild predation with time lags in reproduction and maturation

摘要

A three dimensional (3D) stage-structured predator–prey 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 of delay differential forms of the ODE model are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a Hopf bifurcation when the time lags cross certain 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.