Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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TEMPORAL AND SPATIO-TEMPORAL DYNAMICS OF A MATHEMATICAL MODEL OF HARMFUL ALGAL INTERACTION

  • 발행 : 2009.01.31
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초록

The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings.

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