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Spatiotemporal dynamics in a spatial plankton system. (English) Zbl 1197.92049
Summary: We investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional response. We carried out an analytical study for both one- and two-dimensional systems in detail and found a condition for diffusive instability of locally stable equilibria. Furthermore, we present a theoretical analysis of the processes of pattern formation that involves organism distributions and their interactions of spatially distributed populations with local diffusion. The results of numerical simulations reveal that, by increasing the value of the fish predation rates, the sequence spots $\to$ spot-stripe mixtures $\to$ stripes $\to$ hole-stripe mixtures holes $\to$ wave pattern is observed. Our study shows that the spatially extended model system has not only more complex dynamic patterns in the space, but also spiral waves.
##### MSC:
 92D40 Ecology 35B35 Stability of solutions of PDE 92C15 Developmental biology, pattern formation 34D20 Stability of ODE 65C20 Models (numerical methods) 37N25 Dynamical systems in biology