Turing instability of a diffusive predator-prey model along with an Allee effect on a predator

Modeling biological systems is a significant task in nature. This work concentrates on the relation between two prey species and one predator species model. Our interaction is based on a competition between two preys and one predator, with an additive Allee effect in the predator population. Many investigations have been done in stability properties of the population dynamics. However in this study, we demonstrated population instability as a result of the incorporating diffusive terms in the PDE system and we construct the amplitude equations of stationary patterns using the nonlinear multiple scale analysis approach and Taylor series expansion. Numerical results are also presented to validate our propositions.