A plant-pollinator-pesticide model

Abstract

In this paper, a non-linear mathematical model is proposed and analysed to study the dynamics of plant-pollinator-pesticide interactions. Analysis of the existence of equilibrium points is done. Sufficient conditions for local as well as global stability have been derived. A threshold value of the energetic reward is obtained above which the dynamical system persists uniformly. Further, numerical simulations are performed to confirm the analytic results and to deduce some other important conclusions. It is shown that the plant and pollinator populations support the growth of each other and are mutually dependent when the energetic reward is high. It is observed that equilibrium values of plant and pollinator populations can be maintained for high energetic rewards even though pesticides are present, but at low values of energetic reward, plant population becomes extinct in presence of pesticides.