Global Stability of Cycles: Lotka-Volterra Competition Model With Stocking |
| |
Authors: | Saber Elaydi Abdul-Aziz Yakubu |
| |
Institution: | 1. Department of Mathematics , Trinity University , San Antonio, TX, USA;2. Department of Mathematics , Howard University , Washington, DC, 20059, USA |
| |
Abstract: | In this article, we prove that in connected metric spaces n - cycles are not globally attracting (where n S 2 ). We apply this result to a two species discrete-time Lotka-Volterra competition model with stocking. In particular, we show that an n - cycle cannot be the ultimate life-history of evolution of all population sizes. This solves Yakubu's conjecture but the question on the structure of the boundary of the basins of attractions of the locally stable n - cycles is still open. |
| |
Keywords: | Global Stability Lotka-Volterra Model Yakubu's Conjecture Dual Attractor |
|
|