title: Hierarchical competition models with the Allee effect II: the case of immigration.
abstract: This is part II of an earlier paper that dealt with hierarchical models with the Allee effect but with no immigration. In this paper, we greatly simplify the proofs in part I and provide a proof of the global dynamics of the non-hyperbolic cases that were previously conjectured. Then, we show how immigration to one of the species or to both would, drastically, change the dynamics of the system. It is shown that if the level of immigration to one or to both species is above a specified level, then there will be no extinction region where both species go to extinction.
authors.affiliation: a Department of Mathematics , King Abdul Aziz University , Saudi Arabia.
authors.forename: Laila
authors.initials: L
authors.lastname: Assas
authors.affiliation: b Departement of Mathematics , University of Idaho , 875 Perimeter Drive MS 1136 Moscow, ID 83844 , USA.
authors.forename: Brian
authors.initials: B
authors.lastname: Dennis
authors.affiliation: c Department of Fish and Wildlife Science , Trinity University, One Trinity Place , San Antonio , TX 78212 , USA.
authors.forename: Saber
authors.initials: S
authors.lastname: Elaydi
authors.affiliation: d Department of Mathematics , Trinity University , One Trinity Place, San Antonio , TX 78212 , USA.
authors.forename: Eddy
authors.initials: E
authors.lastname: Kwessi
authors.affiliation: e Department of Space Science , Southwest Research Institute , San Antonio , TX 78238 , USA.
authors.forename: George
authors.initials: G
authors.lastname: Livadiotis
mesh_terms: D003163:Competitive Behavior; D004641:Emigration and Immigration; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics
keywords: Population dynamics; ecology and evolutionary biology