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.