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Spatiotemporal Dynamics in a Spatial Plankton System

Published online by Cambridge University Press:  27 July 2010

R. K. Upadhyay ,
W. Wang  and
N. K. Thakur
R. K. Upadhyay*
Affiliation:
Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India
W. Wang
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433 P.R. China School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang, 325035 P.R.China
N. K. Thakur
Affiliation:
Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826004, India
*
* Corresponding author. E-mail: [email protected]. 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.
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Abstract

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.

Keywords

spatial plankton systempredator-prey interactionglobally asymptotically stablepattern formation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 5: Reaction-diffusion waves , 2010 , pp. 102 - 122
Copyright
© EDP Sciences, 2010

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