Bifurcation in economic grawth model to transformed ode
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Date
2022
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Larbi Tebessi University - Tebessa
Abstract
Our workfocusesonstudyingtwopapersdeeply,wherewescrutinizeanddis-
cuss themainpaperofGuerrinietal.[?], whichisconsideredageneralization
of KrawiecandSzydlowskiwork[?]. Whither,theauthorsinvestigatedthedy-
namics ofthemodi_edKaldormodelandconcludedgivingthemtheresultthat
the limitcyclebehaviorisindependentoftheassumptionthattheinvestment
function iss-shaped.Inthisstudy,asanassumption,supposedthelinearfunc-
tion I(Y ), andonlythetime-delayparameterplayacrucialroleincreatingthe
limit cycle.Also,theyshowedthatforasmalltime-delayparameter,inthelin-
ear approximation,theKaldor_KaleckimodelassumestheformoftheLiénard
equation. Alinearstabilityanalysisincludingthetimedelayisshowntobean
accurate predictorofthecritical T for the_rstbifurcation.As T is increased,
the systembifurcatestothelimitcyclebehavior,thentomultipleperiodicand
aperiodiccyclesoreventuallytendstowardsthechaoticbehaviorviatheperiod
doubling cascaderoutetotheturbulence.
Guerrini etalstudiedapossiblebifurcationexpectedtoachangeofthepa-
rameter valuesoftheKaldor-Kaleckigrowthmodel,which,theyconsidertwo
simplest casesofthreeandfour-dimensionaldynamicalsystems,thatwereob-
tained throughthelinearchaintrickfromtheKaldor-Kaleckigrowthmodel
with distributeddelay.Forbothmodels,theexistenceconditions'oftheHopf
bifurcation withrespecttothetimedelayparameterandtherateofgrowthpa-
rameter areestablished.Finally,wediscussthenumericalstudyintheprevious
papers
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Keywords
Modèledecroissanceéconomique,modèledeKaldor-Kalecki,fonc- tion d'investissement,paramètredetempsderetard,tempsderetarddistribué, bifurcation deHopf, Economic growthmodel,Kaldor_Kaleckimodel,Investmentfunc- tion, time-delayparameter,distributedtimedelay,Hopfbifurcation