Lethal effect of insecticides on marine ecosystem due to agricultural runoff

Abstract

We present a continuous time model of the dynamics of organisms in a food chain in presence of a constant rate of flow of an input limiting nutrient. The organisms at the first trophic level are growing on the limiting nutrient, whereas the organisms at the second trophic level feed on the organism at the first trophic level only. An external lethal inhibitor is introduced in the system, accelerating the death of the organisms at the highest trophic level. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the species associated with the system cannot thrive even in absence of competition. Also, we prove that under certain conditions the system is permanent in presence of all the organisms and obtain conditions for permanence under which one of the two organisms is extinct. Local stability of the system is obtained in absence of sensitive species and in presence of both sensitive and resistant species. Moreover, it is shown that the system undergoes Hopf bifurcation if the half saturation constant crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.