Qualitative Analysis of Bifurcation: The First Border Steady-State Solution

Abstract

This paper examines the bifurcation analysis of two interacting ecological species in a qualitative manner. In the modelling of competition interaction between two ecological species, when the daily intrinsic growth rate  is varied while other model parameters are fixed, the fundamental qualitative changes of the borders steady-state solution  are studied. This steady-state solution is stable if   and  provided  is a positive parameter and  is one of the model parameters. It passes through a bifurcation point  and  and is unstable if   and .