Dynamical properties of a stage structured three-species model with intra-guild predation

This paper considers a stage-structured three species model with intra-guild predation (IGP). First, we show local and global stability of IGP model. It is known that introduction of IGP in tritrophic food chain can destabilize the system. So in order to ensure survival of all species for all future time, we show a necessary and sufficient condition for permanence of IGP model. Next, we consider the IGP model with a stage structure for predator. The model uses time delay to express a maturation period and a through-stage survival rate for the predator. By using stability switch criteria which can provide practical guidelines that combine graphical information with analytical work, we can show that the delay can stabilize the IGP model.