Pattern formation for a model of plankton allelopathy with cross-diffusion

In this paper, we develop a theoretical framework for investigating spatial patterns on plankton allelopathy with cross-diffusion. We show that under some conditions the cross-diffusion is able to induce the Turing instability, which is further confirmed by the numerical simulations. Moreover, applying the Leray–Schauder degree theory, we demonstrate that the cross-diffusion leads to an inhomogeneous stationary pattern provided with even stronger conditions. Finally, the wavenumber and the type of pattern selection are computed numerically. Our theoretical results of the spatial pattern are coincident with the experimental observations.