Comparative analysis of nonlocal interactions in a two-dimensional prey-predator model with Allee effect in predator...

This article presents a comprehensive investigation into a two-dimensional nonlocal spatiotemporal model, incorporating a generalist predator and addressing the Allee effect in predator growth. We study two types of nonlocality. First, by introducing nonlocality in the intrinsic growth of prey, we explore its effects on prey population distribution and stability. Second, incorporating nonlocality into the functional response enables us to study the predator-prey interactions across spatial distances. Our study underscores the diverse and contrasting effects of both types of nonlocal interactions on ecological pattern formation. Comparing the local and nonlocal models highlights the significant impact of nonlocal interactions on spatial patterns and system dynamics, emphasizing the importance of considering the nonlocal effects in ecological and biological models to understand spatial pattern formation and system stability. This study is among the first to investigate two-dimensional nonlocal models with the tophat kernel. Furthermore, by imposing restrictions on the nonlocal interaction coefficient, the two-dimensional analytical analysis is effectively reduced to a one-dimensional framework, enabling a simplified exploration of the system through both analytical and numerical simulations.