Geodesic
Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 34C11, 34C23, 34D08, 34D20, 35Q92, 92B05, 92D40
Keywords: phytoplankton dynamics, reaction-diffusion equation, local stability, Hopf-bifurcation, diffusion-driven instability, spatial pattern formation 
@article{EJDE_2012__2012__a20,
     author = {Baghel,  Randhir Singh and Dhar,  Joydip and Jain,  Renu},
     title = {Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1243.34062},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a20/}
}
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%A Jain,  Renu
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%J Electronic journal of differential equations
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%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a20/
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%F EJDE_2012__2012__a20
Baghel,  Randhir Singh; Dhar,  Joydip; Jain,  Renu. Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a20/