A Mathematical Model for Population Density Dynamics of Weed-Crop Competition

Abstract

A model for the dynamics of homogeneous population competition between two species of weeds and a crop is formulated to gain in-sight into the behaviour of crop growing with weeds. We used assumptions based upon reasonable biological process to derive from single weed model equation, the systems of difference equations that described the dynamics of weed-crop competition. Steady- state solutions of the model are obtained and analyzed for local stability or otherwise. The results show that the extinction steady state is not stable without control and the conditions for stability of two plants steady-states are given. The weed-crop coexistence steady state of our model is locally asymptotically stable. Besides, the graphical profile of the model shows that the crop’s growth may be stagnated by the weeds’ densities. Hence, we conclude that the crop’s growth may be stagnated, but survive in the mixture of the two species of weeds. However, application of effective control measure to eradicate the two weeds species will enhance crop growth at its optimum capacity.