Parameter based stability analysis of generalized mathematical model with delay of competition between two species

Abstract

Two of the importance of stability analysis is investigating the influence of the parameters on stability of equilibrium points of mathematical model and identifying the region of stability in the plane of the parameters. This study is aimed at identifying region of stability in the plane of parameters and setting conditions of stability of equilibrium points of a generalized mathematical model with delay of two species characterized by an interaction of the type competition. d-decomposition method, direct calculation of eigenvalues and simulation of the model for different numerical values using computing software MATLAB is employed. As a result, different locally asymptotically stability conditions were established and stability regions in the parameter plane were identified for different specific values. The practicality of the method and the results were confirmed by using specific mathematical models of the type under consideration. The parameter based stability analysis conducted on the specific model revealed that the result of this research can be used to find parameter domain for which an interior equilibrium point of a given dynamic system of the type under discussion is locally asymptotically stable.