Global dynamics of Lotka-Volterra equations characterizing multiple predators competing for one prey

Abstract

This paper studies global dynamics of a class of n-dimensional Lotka–Volterra systems, in which (n−1) predator species competing for a single prey species. Using dynamical system theory, we show global dynamical behavior of the n species in the first octant, and prove necessary and sufficient conditions for the principle of competitive exclusion to hold, which leads to an extension of Volterra's principle and the work by Llibre and Xiao (2014) [5]. These results provide biological insight in coevolution of predators.