Hopf bifurcation in the IS-LM business cycle model with time delay

The distinction between investment decisions and implementation leads us to formulate a new IS-LM business cycle model. It is shown that the dynamics depends crucially on the time delay parameter - the gestation time period of investment. The Hopf bifurcation theorem is used to predict the occurrenc...

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Bibliographic Details
Main Author:	Jianping Cai
Format:	Article
Language:	English
Published:	Texas State University 2005-02-01
Series:	Electronic Journal of Differential Equations
Subjects:	Hopf bifurcation business cycle IS-LM model time delay.
Online Access:	http://ejde.math.txstate.edu/Volumes/2005/15/abstr.html

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spelling	doaj-f6520c162ae943829b33b6c7db6045b32020-11-24T22:28:04ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-02-0120051516Hopf bifurcation in the IS-LM business cycle model with time delayJianping CaiThe distinction between investment decisions and implementation leads us to formulate a new IS-LM business cycle model. It is shown that the dynamics depends crucially on the time delay parameter - the gestation time period of investment. The Hopf bifurcation theorem is used to predict the occurrence of a limit cycle bifurcation for the time delay parameter. Our analysis shows that the limit cycle behavior is independent of the assumption of nonlinearity of the investment function. An example is given to verify the theoretical results.http://ejde.math.txstate.edu/Volumes/2005/15/abstr.htmlHopf bifurcationbusiness cycleIS-LM modeltime delay.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jianping Cai
spellingShingle	Jianping Cai Hopf bifurcation in the IS-LM business cycle model with time delay Electronic Journal of Differential Equations Hopf bifurcation business cycle IS-LM model time delay.
author_facet	Jianping Cai
author_sort	Jianping Cai
title	Hopf bifurcation in the IS-LM business cycle model with time delay
title_short	Hopf bifurcation in the IS-LM business cycle model with time delay
title_full	Hopf bifurcation in the IS-LM business cycle model with time delay
title_fullStr	Hopf bifurcation in the IS-LM business cycle model with time delay
title_full_unstemmed	Hopf bifurcation in the IS-LM business cycle model with time delay
title_sort	hopf bifurcation in the is-lm business cycle model with time delay
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2005-02-01
description	The distinction between investment decisions and implementation leads us to formulate a new IS-LM business cycle model. It is shown that the dynamics depends crucially on the time delay parameter - the gestation time period of investment. The Hopf bifurcation theorem is used to predict the occurrence of a limit cycle bifurcation for the time delay parameter. Our analysis shows that the limit cycle behavior is independent of the assumption of nonlinearity of the investment function. An example is given to verify the theoretical results.
topic	Hopf bifurcation business cycle IS-LM model time delay.
url	http://ejde.math.txstate.edu/Volumes/2005/15/abstr.html
work_keys_str_mv	AT jianpingcai hopfbifurcationintheislmbusinesscyclemodelwithtimedelay
_version_	1725748110495318016

Hopf bifurcation in the IS-LM business cycle model with time delay

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