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Full-Text Articles in Physical Sciences and Mathematics
Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu
Global Stability Of Cycles: Lotka-Volterra Competition Model With Stocking, Saber Elaydi, Abdul-Aziz Yakubu
Saber Elaydi
In this article, we prove that in connected metric spaces k - cycles are not globally attracting (where k>2). We apply this result to a two species discrete-time Lotka-Volterra competion model with stocking. In particular, we show that an k-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 attraction of the locally stable n-cycles is still open.
Bifurcation And Invariant Manifolds Of The Logistic Competition Model, Malgorzata Guzowska, Rafael Luis, Saber Elaydi
Bifurcation And Invariant Manifolds Of The Logistic Competition Model, Malgorzata Guzowska, Rafael Luis, Saber Elaydi
Saber Elaydi
In this paper we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important center manifolds, and study their bifurcation. Saddle-node and period doubling bifurcation route to chaos is exhibited via numerical simulations.