Inthispaperwestudydeterministic,
finite dimensional, continuous,
as wellas discrete
time populationinvasionmodels. Theabilityof anewlyintroducedpopulation, either a newspeciesor a reproductivelyisolatedsubpopulationofoneofthealreadypresentspecies, tosettle in thecommunityreliesuponthebasicreproduction ratiooftheinvader,
R0. When R0 exceeds 1, theinvadingpopulationmeetswithsuccess, andwhen R0 isbelow 1,theinvasionfails. Theaimofthispaperistoinvestigatethepossibleeffectsofaninvasionwhentheparametersof a model are varied so that R0 oftheinvadingpopulationpassesthevalue
1. We argue thatpopulationinvasionmodels, regardlessofthebiologythatunderliesthem, takea specificformthatsignificantlysimplifiesthecentermanifoldanalysis.Wemake a uniformstudyofecological,
adaptivedynamicsanddiseasetransmissionmodelsand derive a simple formula forthedirectionofbifurcationfrom a steadystate
in whichonlytheresidentpopulations
are present. Furthermore, we observe thatamongthosebifurcationparametersthatsatisfy a certaincondition, weacquirethesamedirectionofbifurcation. Theobtainedmathematicalresults areusedtogaininsightintothebiologyofinvasions.
Thetheoryisillustrated by severalexamples.
UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno
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