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Zbl 1197.92049
Upadhyay, R.K.; Wang, W.; Thakur, N.K.
Spatiotemporal dynamics in a spatial plankton system. (English)
[J] Math. Model. Nat. Phenom. 5, No. 5, 102-122 (2010). ISSN 0973-5348; ISSN 1760-6101/e

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 2000:: *92D40 Ecology
35B35 Stability of solutions of PDE
92C15 Developmental biology, etc.
34D20 Lyapunov stability of ODE
65C20 Models (numerical methods)
37N25 Dynamical systems in biology

Keywords: spatial plankton system; predator-prey interaction; globally asymptotically stable; pattern formation

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Zentralblatt MATH Berlin [Germany]