Impact of allee effect and spatiotemporal spread on a predator-prey model

Abstract

Among the many variables that could affect population dynamics in predator-prey interactions are the Allee effect, the fear effect, cooperative hunting, and group dynamics. Analysing these elements in predator-prey improves the model's realism. In this work, we have put forth a model of predator-prey cooperation that produces herd dynamics and the Allee effect on the population of prey. We have investigated the Allee effect using temporal analysis. In order to investigate the importance of random movement and the type of geographical structure that the population creates as a result of random mobility, we have expanded the research to include spatiotemporal analysis. We first explain the existence and positivity of the proposed model, and then we apply the Routh Hurwitz criterion to examine the stability of the current equilibrium points. Using Hopf-bifurcation at the coexistence equilibrium point, the temporal analysis is performed with the Allee threshold ($a$) taken into consideration as adjustable factors. We investigate the spatial model's stability, upon the introduction of diffusion and develop the Turing instability condition leading to several types of Turing patterns. Numerical simulations are then used to confirm the analytical conclusions. The stability of the model is dependent on spatiotemporal spread, and Allee effect according to the results of the theoretical study and numerical simulation.