Electron. J. Diff. Equ., Vol. 2012 (2012), No. 21, pp. 1-12.

Bifurcation and spatial pattern formation in spreading of disease with incubation period in a phytoplankton dynamics

Randhir Singh Baghel, Joydip Dhar, Renu Jain

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.

Show me the PDF file (470 KB), TEX file, and other files for this article.

Randhir Singh Baghel
School of Mathematics and Allied Science
Jiwaji University
Gwalior (M.P.)-474011, India
email: randhirsng@gmail.com
Joydip Dhar
Department of Applied Sciences
ABV-Indian Institute of Information Technology and Management
Gwalior-474010, India
email: jdhar@iiitm.ac.in
Renu Jain
School of Mathematics and Allied Science
Jiwaji University
Gwalior (M.P.)-474011, India
email: renujain3@rediffmail.com

Return to the EJDE web page