About: BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper a 3-dimensional system of autonomous differential equations is studied. It can be interpreted as an idealized macroeconomic model with foreign capital investment or an idealized model of the firm profit. The system has three endogenous variables with only one non-linear term and can be also interpreted as an extended van der Pol's equation. It's shown that this simple system covers several types of bifurcations: both supercritical and subcritical Hopf bifurcation and generalized Hopf bifurcation as well, the limit cycle exhibits period-doubling bifurcation as a route to chaos. Some results are analytical and those connected with chaotic motion are computed numerically with continuation programs Content, Xppaut and Maple. We present conditions for stability of the cycles, hysteresis, explore period doubling and using Poincare mapping show a three period cycle that implies chaos. In this paper a 3-dimensional system of autonomous differential equations is studied. It can be interpreted as an idealized macroeconomic model with foreign capital investment or an idealized model of the firm profit. The system has three endogenous variables with only one non-linear term and can be also interpreted as an extended van der Pol's equation. It's shown that this simple system covers several types of bifurcations: both supercritical and subcritical Hopf bifurcation and generalized Hopf bifurcation as well, the limit cycle exhibits period-doubling bifurcation as a route to chaos. Some results are analytical and those connected with chaotic motion are computed numerically with continuation programs Content, Xppaut and Maple. We present conditions for stability of the cycles, hysteresis, explore period doubling and using Poincare mapping show a three period cycle that implies chaos. (en)
Title	BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS (en)
skos:prefLabel	BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS (en)
skos:notation	RIV/00216224:14310/09:00035397!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	S
http://linked.open...avai/riv/aktivity	S
http://linked.open...iv/cisloPeriodika	53
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Přibylová, Lenka
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	305052
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/09:00035397
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hopf bifurcation; period doubling; chaos (en)
http://linked.open.../riv/klicoveSlovo	Hopf bifurcation period doubling chaos
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[97A456907057]
http://linked.open...i/riv/nazevZdroje	Electronic Journal of Differential Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	2009
http://linked.open...iv/tvurceVysledku	Přibylová, Lenka
issn	1072-6691
number of pages	21 (xsd:int)
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS

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