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Alexander B. Medvinsky \emph{et al} [A. B. Medvinsky, I. A. Tikhonova, R. R.Aliev, B.-L. Li, Z.-S. Lin, and H. Malchow, Phys. Rev. E \textbf{64}, 021915(2001)] and Marcus R. Garvie \emph{et al} [M. R. Garvie and C. Trenchea, SIAMJ. Control. Optim. \textbf{46}, 775-791 (2007)] shown that the minimalspatially extended reaction-diffusion model of phytoplankton-zooplankton canexhibit both regular, chaotic behavior, and spatiotemporal patterns in a patchyenvironment. Based on that, the spatial plankton model is furtherlyinvestigated by means of computer simulations and theoretical analysis in thepresent paper when its parameters would be expected in the case of mixedTuring-Hopf bifurcation region. Our results show that the spiral waves exist inthat region and the spatiotemporal chaos emerge, which arise from the far-fieldbreakup of the spiral waves over large ranges of diffusion coefficients ofphytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising fromthe far-field breakup of spiral waves does not gradually involve the wholespace within that region. Our results are confirmed by means of computationspectra and nonlinear bifurcation of wave trains. Finally, we give someexplanations about the spatially structured patterns from the community level.

Emergence of spatiotemporal chaos driven by far-field breakup of spiral waves in the plankton ecological systems