Original Research ArticleSpatio-temporal pattern formation in Rosenzweig-MacArthur model: Effect of nonlocal interactions

•Spatio-temporal Rosenzweig-MacArthur model with a nonlocal term is studied.•Nonlocal consumption of resources by prey is considered.•Analytical condition for Turing bifurcation is derived.•Stationary and dynamic patterns are obtained through numerical simulations.•Appropriate bifurcation diagrams are prepared to explain the transition of patterns.

Spatio-temporal pattern formation in reaction-diffusion models of interacting populations is an active area of research due to various ecological aspects. Instability of homogeneous steady-states can lead to various types of patterns, which can be classified as stationary, periodic, quasi-periodic, chaotic, etc. The reaction-diffusion model with Rosenzweig-MacArthur type reaction kinetics for prey-predator type interaction is unable to produce Turing patterns but some non-Turing patterns can be observed for it. This scenario changes if we incorporate non-local interactions in the model. The main objective of the present work is to reveal possible patterns generated by the reaction-diffusion model with Rosenzweig-MacArthur type prey-predator interaction and non-local consumption of resources by the prey species. We are interested in the existence of Turing patterns in this model and in the effect of the non-local interaction on the periodic travelling wave and spatio-temporal chaotic patterns. Global bifurcation diagrams are constructed to describe the transition from one pattern to another one.