Modeling the impact of competitive coefficient of two interacting herbivores in a mild environment on resource biomass

Abstract

The paper formulates and studies a non-linear first-order mathematical model to understand the dynamics of the impact of resource biomass on two competing resource-dependent interacting biological inter-specific species. Analysis of the model was performed by finding the equilibrium points and their dynamic behaviours with the conditions for stability and instability of the system established. As a consequence, the analytic solution obtained was tested using parameter values as given by George, (2019) for the simulation of the system (3.1)-(3.3) and MATLAB ODE45 was used for simulation as depicted in figures 1,2,3 and 4 and the results indicate that a biodiversity gain could be achieved where the two interacting species co-exist as shown in figure 5. This is possible where there is a steady nutrient supply for the two species (Rabbit and Goat) and the resource biomass (Grass) and this will require appropriate farm management practices and policies to sustain the ecosystem of discussion.