Stability Analysis and Numerical Solutions of a Competition Model with the Effects of Distribution Parameters

A system of two nonlinear differential equations in mathematical biology is considered. These models are originally stimulated by population models in biology when solutions are required to be non-negative, but the ordinary differential equations can be understood outside of this conventional scope of population models. The focus of this paper is on the use of linearization techniques, and Hartman Grobman theory to analyze nonlinear differential equations. We provide stability analysis and numerical solutions for these models that describe behaviors of solutions based only on the parameters used in the formulation of the systems