Photosynthesis rate, salinity induced grazing rate and gestation delay as determinants of the dynamics of a realistic food chain model: a stochastic approach

Abstract

Impact of photosynthesis rate of phytoplankton, salinity induced grazing rate of zooplankton and gestation delay of zooplankton and fish population are considered in the present study. Models with delay are much more realistic, as in reality time delays occur in almost every biological situation and assume to be one of the reasons of regular fluctuations in population density. Reproduction of predator after consuming prey is not instantaneous, but mediated by some time lag required for gestation. It is observed that there is stability switches and Hopf bifurcation occurs when the delay crosses some critical value. It is observed that the quantitative level of abundance of system population depends crucially on the delay parameter if the gestation period exceeds some critical value. Also, environmental stochasticity in the form of Gaussian whitenoise, plays a significant role to describe the system and its values. Numerical examples are also support the model assumption and analytical results.