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Turing patterns in a modified Lotka-Volterra model. (English) Zbl 1222.92065

Summary: We consider a modified Lotka-Volterra model, widely known as the Bazykin model, which is the MacArthur-Rosenzweig (MR) model that includes a prey-dependent response function and is modified with the inclusion of intraspecies interactions. We show that a quadratic intra-prey interaction term, which is the most realistic nonlinearity, yields sufficient conditions for Turing patterns. For the Bazykin model we find the Turing region the in parameter space and Turing patterns in one dimension.

Editorial remark: Note that the content of the article actually argues the intra-predator interaction term as the crucial factor instead of yielding sufficient conditions.

92C15Developmental biology, pattern formation