A Lotka-Volterra competition model and its global convergence to a definite axial equilibrium

摘要

We consider a four-species model based on competition and show that the whole four-species system collapses to a definite single species equilibrium at its carrying capacity. To do so, we use the results of Hirsch [4], Van Den Driessche and Zeeman [20], Hofbauer and Sigmund [5], and the product theorem of the Conley connection matrix theory by Mischaikow and Reineck [10]. [References: 22]