Theoretical bifurcation analysis of a biological interspecific competition interaction

Abstract

Bifurcation analysis of a biological interaction model can provide useful information for ecological functioning and stability. In this paper, we will study the fundamental changes in the qualitative behaviour of the solution trajectories due to a variation of an intrinsic growth rate when other model parameters are fixed. Our contribution is as follows: the trivial steady-state solution is a stable node when p1 < 0 and d < 0, and a saddle when p1 > 0 and d > 0. The transcritical bifurcation points where the trivial steady-state solution changes stability are p1 = 0 and d = 0.