Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 98, pp. 1-15.

Title: Stochastically perturbed allelopathic phytoplankton model

Authors: Syed Abbas (Univ. degli Studi di Bologna, Italy)
         Malay Banerjee (Indian  Inst. of Technology, Kanpur, India)

Abstract: 
 In this article we have considered a stochastic delay differential
 equation model for two species competitive phytoplankton system
 with allelopathic stimulation. We have extended the deterministic
 model system to a stochastic delay differential equation model
 system by incorporating multiplicative white noise terms in the
 growth equations for both species. We have studied the mean square
 stability of coexisting state using a suitable Lyapunov functional.
 Numerical simulation results are provided to validate the
 analytical findings.
 
Submitted May 18, 2010. Published July 21, 2010.
Math Subject Classifications: 93E15, 34C23, 37B25, 34K50.
Key Words: Stability; bifurcation; Lyapunov functional;
           stochastic perturbation