Bifurcation scenario of Turing patterns in prey-predator model with nonlocal consumption in the prey dynamics

A prey-predator model with a sexual reproduction in prey population and nonlocal consumption of resources by prey in two spatial dimensions is considered. Patterns produced by the model without nonlocal terms and periodic boundary conditions are studied first. Then, Turing patterns induced by the nonlocal interaction (see Banerjee et al. (2018) [1]) in the two dimensional space are explored along with the effects of the nonlocal interaction range on the resulting patterns under proper parametric restrictions. The Turing bifurcation conditions for the nonlocal model are derived analytically and bifurcation scenario of stationary hotspot pattern generated from the homogeneous steady-state are studied in detail, both analytically and numerically. Also, conversion of periodic and aperiodic solutions exhibited by the local model into stationary Turing pattern as an effect of the nonlocal interaction term is also explored. The resulting patterns are stationary when the range of nonlocal interactions are significantly large. © 2020