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Full-Text Articles in Other Applied Mathematics
General Allee Effect In Two-Species Population Biology, Saber Elaydi
General Allee Effect In Two-Species Population Biology, Saber Elaydi
Saber Elaydi
The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator-prey models. The study is restricted to the strong Allee effect caused by an interspecific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a "phase space core" of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar …
Bifurcation And Invariant Manifolds Of The Ricker Competition Model, Saber Elaydi
Bifurcation And Invariant Manifolds Of The Ricker Competition Model, Saber Elaydi
Saber Elaydi
We study the stability and bifurcation of all equilibrium points, including extinction, exclusion, and coexistence points. Stable , unsgtable are computed. Moreover, for the nonhyperbolic cases, we computed the center manifolds and determine their stability or lack of it thereof.