Structural stability analysis of an algal bloom mathematical model in tropic interaction

The paper deals with the dynamical behavior of plankton population ecosystem, mainly found in Sunderban mangrove area. The ecosystem is represented by a set of two dimensional non-linear differential equations involving zooplankton-phytoplankton population. Plankton populations undergo dramatic changes in marine ecology. We propose a description of plankton communities as excitable systems which resemble the behavior of excitable media. The delay parameter dependency of the various ‘excitable’ phenomena, trigger mechanism, threshold, and slow recovery, is clear, and permits ready investigation of the influence of properties of the physical environment, including variations in nutrient fluxes, temperature or population levels. We have analyzed the stability and bifurcation of the model system with and without delay. We have shown the existence and uniqueness of limit cycles in the rapid growth of the plankton population. We also studied the model system into a stochastic one, by incorporating random fluctuations of the environment. And we study the stochastic stability of the dynamical system in mean square sense around the interior equilibrium.