Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 21, pp. 1-12.

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

Authors: Randhir Singh Baghel (Jiwaji Univ., Gwalior, India)
         Joydip Dhar (ABV-Indian Institute of Information, Gwalior, India)
	 Renu Jain   (Jiwaji Univ., Gwalior, India)

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 02, 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.