Cross diffusion induced spatiotemporal pattern in diffusive nutrient–plankton model with nutrient recycling

Abstract

This paper presents a mathematical model of spatiotemporal interaction between the nutrient and phytoplankton. The interaction among the constituents in nutrient–phytoplankton system has been considered with Holling type-III functional response and nutrient recycling. We have also considered the effect of cross and self-diffusion in the system. The stability analysis of non-spatial and spatial systems have been studied. We have used simulation techniques to generate patterns for cross and self-diffusive systems. We have performed the numerical simulations and observed the effect of time evolution, cross-diffusion and rate of toxin release by phytoplankton on the density distribution of species. This phenomenon is elaborately discussed in this manuscript by introducing weakly nonlinear analysis. We also introduce amplitude equations which describe the structural interpretation and the stability of Turing pattern for nutrient–phytoplankton system. Amplitude equation is derived by using multiple-scale analysis. Cross-diffusion plays an important role in Turing instability and the formation of spot, stripe and spot–stripe like patterns. It suggests the positive environmental outcomes from nutrient recycling and spatial distribution of phytoplankton in the real world situation.