Dynamics of intraguild predation with intraspecies competition.

Intraguild predation, the most fundamental mechanism in food webs with three species, is a mix of competition and predation in which two species that are participating in a predator–prey relationship are also competing for a common resource. We investigate an intraguild predation model by considering three population, namely shared resource, IG-prey and IG-predator by using a coupled system of ordinary differential equations and use Holling type II functional response between IG-prey and IG-predator. The dynamic properties of the proposed model are analyzed, including positivity, boundedness, uniform persistent, the existence and stability of the equilibria and Hopf bifurcation. We derive the sufficient conditions for the persistence and extinction of all feasible scenarios for the proposed model by providing a comprehensive view of their global stability. Our results reveal that the attacking rate and decay rate of the intraguild-predator can promote the formation of the stability of the model by transforming it from an unstable state to a stable state. The region of stability around interior equilibrium and around IG-predator free equilibrium has been obtained in terms of the attacking rate and decay rate of the intraguild-predator. The parameters interval for the coexistence of the three species has been determined. Our theoretical analysis and numerical illustrations demonstrate that intraguild predation model is prone to have coexistence of all the three populations. [ABSTRACT FROM AUTHOR]