An Extension of Two Species Lotka-Volterra Competition Model

Abstract

Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Volterra competition model. This describes two competitive species for a single resource which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource. Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.