Inthispaperweinvestigate long-termdynamicsofthemostbasicmodelforstage-structuredpopulations, in whichtheper capita transitionfromthejuvenileintotheadultclassisdensitydependent.Themodelisrepresented
by anautonomoussystemoftwononlineardifferentialequationswithfourparametersfor a single population.Wefindthattheinteractionofintra-adultcompetitionandintra-juvenilecompetitiongivesrisetomultipleattractors, oneofwhich canbe oscillatory. A detailednumericalstudyreveals a richbifurcationstructureforthistwo-dimensional
system, originatingfrom a degenerateBogdanov--Takens(BT) bifurcationpointwhenoneparameteriskeptconstant.
Dependingonthevalueofthisfixedparameter, thecorresponding triplecriticalequilibrium has eitheranelliptic sector oritisa topologicalfocus, whichisdemonstrated
by thenumerical normalformanalysis. Itisshownthatthe canonical unfoldingofthecodimension-three BT pointrevealstheunderlyingdynamicsofthemodel. Certainnewfeaturesofthisunfolding
in theellipticcase,
which are important in applicationsbuthavebeenoverlookedin availabletheoreticalstudies, are established. Variousthree-, two-, andone-parameterbifurcationdiagramsofthemodel are presentedandinterpretedin
biologicalterms.
UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno
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