Study of a diffusive intraguild predation model

The present study analyzes an intraguild predation model, which combines predation with competition. This model has food webs with a fundamental three-species structure in which two populations are associated not only by prey–predator relationships but also by the competition between them for a common prey. The growth of prey is assumed to follow the Smith growth function, and self-diffusion is taken into consideration under zero-flux boundary condition. The feasible equilibria and their stability in temporal system are explained. The stability of positive steady state (PSS) in the PDE system is also discussed. An a priori estimate for positive steady state (PSS) is performed with the help of Harnack’s inequality and maximum principle. Under certain conditions, the non-existence of non-constant PSS are obtained by the Poincare inequality, while the Leray–Schauder theory explains the emergence of non-constant PSS, which leads the system to develop stationary patterns. This article represents a theoretical framework that describes the creation of patterns for the intraguild predation model due to the movement of the species.