Spatiotemporal Dynamics in a Spatial Plankton System
R. K. Upadhyay1*, W. Wang2,3 and N. K. Thakur1
Department of Applied Mathematics, Indian School of Mines,
Dhanbad, 826004, India
2 School of Mathematical Sciences, Fudan University, Shanghai, 200433 P.R. China
3 School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, 325035 P.R.China
* Corresponding author. E-mail:
email@example.com. Present Address is: Institute of Biology,
Department of Plant Taxonomy and Ecology, Research group of Theoretical Biology and
Ecology, Eötvös Lorand University, H-1117, Pazmany P.S. 1/A, Budapest, Hungary.
In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially distributed population with local diffusion. The results of numerical simulations reveal that, on increasing the value of the fish predation rates, the sequences spots → spot-stripe mixtures → stripes → hole-stripe mixtures holes → 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 has spiral waves.
Mathematics Subject Classification: 92C15 / 92D25 / 92D40 / 34D20
Key words: spatial plankton system / predator-prey interaction / globally asymptotically stable / pattern formation
© EDP Sciences, 2010