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.

考虑在两个空间维度上具有猎物种群有性繁殖和猎物非本地消耗资源的猎物-捕食者模型。首先研究由模型产生的没有非局部项和周期边界条件的模式。然后，在适当的参数限制下，探索了二维空间中由非局部相互作用引起的图灵模式（参见Banerjee et al。（2018）[1]），以及非局部相互作用范围对所得模式的影响。通过分析得出非局部模型的图灵分支条件，并从分析和数值上详细研究了由均匀稳态产生的稳态热点模式的分支情况。也，还探讨了由于非局部相互作用项的影响，将局部模型所显示的周期和非周期解转换为平稳的图灵模式。当非局部相互作用的范围很大时，结果模式是固定的。