Spatiotemporal Dynamics in a Spatial Plankton System

R. K. Upadhyay; W. Wang; N. K. Thakur

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 5, page 102-122
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Upadhyay, R. K., Wang, W., and Thakur, N. K.. "Spatiotemporal Dynamics in a Spatial Plankton System." Mathematical Modelling of Natural Phenomena 5.5 (2010): 102-122. <http://eudml.org/doc/197652>.

@article{Upadhyay2010,
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.},
author = {Upadhyay, R. K., Wang, W., Thakur, N. K.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {spatial plankton system; predator-prey interaction; globally asymptotically stable; pattern formation},
language = {eng},
month = {7},
number = {5},
pages = {102-122},
publisher = {EDP Sciences},
title = {Spatiotemporal Dynamics in a Spatial Plankton System},
url = {http://eudml.org/doc/197652},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Upadhyay, R. K.
AU - Wang, W.
AU - Thakur, N. K.
TI - Spatiotemporal Dynamics in a Spatial Plankton System
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/7//
PB - EDP Sciences
VL - 5
IS - 5
SP - 102
EP - 122
AB - 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.
LA - eng
KW - spatial plankton system; predator-prey interaction; globally asymptotically stable; pattern formation
UR - http://eudml.org/doc/197652
ER -

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