Deterministic and Stochastic Dynamics of a Competitive Phytoplankton Model with Allelopathy

Allelopathic stimulators have some stabilizing role for the interaction between two or more competitive phytoplankton species within aquatic environment. Various models within deterministic environment are examined by several researchers to understand the role of allelo-chemicals to shape the dynamic behavior within deterministic environment. As plankton species are available within aquatic environment so they are subjected to environmental driving forces. In the present paper we have considered an existing and well established two-species competitive phytoplankton model where one species is toxic. We have revealed various interesting dynamical features of the model which were overlooked in the earlier studies. The stochastic model considered in this paper is obtained from the deterministic model by introducing multiplicative white noise terms. For the stochastic model, we have established the existence of global solution which ensures positivity and boundedness of the solution starting from an interior point of first quadrant in presence of environmental driving forces. Bounds for different order moments of solution are obtained and used to prove the stochastic boundedness of solution. The sufficient conditions for stochastic permanence are obtained and verified with the help of numerical examples. Analytical results are interpreted from ecological point of view. © 2013 Foundation for Scientific Research and Technological Innovation.