Randhir Singh Baghel, Joydip Dhar, Renu Jain
Abstract:
In this article, we propose a three dimensional mathematical model of
phytoplankton dynamics with the help of reaction-diffusion equations
that studies the bifurcation and pattern formation mechanism.
We provide an analytical explanation for understanding phytoplankton
dynamics with three population classes: susceptible, incubated, and infected.
This model has a Holling type II response function for the population
transformation from susceptible to incubated class in an aquatic ecosystem.
Our main goal is to provide a qualitative analysis of Hopf bifurcation
mechanisms, taking death rate of infected phytoplankton as bifurcation
parameter, and to study further spatial patterns formation due to spatial
diffusion. Here analytical findings are supported by the results of numerical
experiments. It is observed that the coexistence of all classes of
population depends on the rate of diffusion. Also we obtained the
time evaluation pattern formation of the spatial system.
Submitted July 25, 2011. Published February 2, 2012.
Math Subject Classifications: 34C11, 34C23, 34D08, 34D20, 35Q92, 92B05, 92D40.
Key Words: Phytoplankton dynamics; reaction-diffusion equation;
local stability; Hopf-bifurcation; diffusion-driven instability;
spatial pattern formation.
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Randhir Singh Baghel School of Mathematics and Allied Science Jiwaji University Gwalior (M.P.)-474011, India email: randhirsng@gmail.com |
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Joydip Dhar Department of Applied Sciences ABV-Indian Institute of Information Technology and Management Gwalior-474010, India email: jdhar@iiitm.ac.in |
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Renu Jain School of Mathematics and Allied Science Jiwaji University Gwalior (M.P.)-474011, India email: renujain3@rediffmail.com |
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