Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function

Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function

In this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee that...

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Main Authors: Yingkang Xie, Zhen Wang, Bo Meng
Format: Article
Language:English
Published: MDPI AG 2019-09-01
Series:Mathematics
Subjects:
business cycle model
stability
time delay
time-fractional-order
Hopf bifurcation
Online Access:https://www.mdpi.com/2227-7390/7/9/846
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spelling doaj-c3aaa3cc00194fbdab412651bcac56b92020-11-25T02:42:11ZengMDPI AGMathematics2227-73902019-09-017984610.3390/math7090846math7090846Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment FunctionYingkang Xie0Zhen Wang1Bo Meng2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaIn this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee that the positive equilibrium point of DTFOM is locally stable. In addition, Hopf bifurcation is obtained by a new method, where the time delay is regarded as the bifurcation parameter. Finally, a numerical example of DTFOM is given to verify the effectiveness of the proposed model and methods.https://www.mdpi.com/2227-7390/7/9/846business cycle modelstabilitytime delaytime-fractional-orderHopf bifurcation
collection DOAJ
language English
format Article
sources DOAJ
author Yingkang Xie
Zhen Wang
Bo Meng
spellingShingle Yingkang Xie
Zhen Wang
Bo Meng
Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
Mathematics
business cycle model
stability
time delay
time-fractional-order
Hopf bifurcation
author_facet Yingkang Xie
Zhen Wang
Bo Meng
author_sort Yingkang Xie
title Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
title_short Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
title_full Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
title_fullStr Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
title_full_unstemmed Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function
title_sort stability and bifurcation of a delayed time-fractional order business cycle model with a general liquidity preference function and investment function
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-09-01
description In this paper, the business cycle (BC) is described by a delayed time-fractional-order model (DTFOM) with a general liquidity preference function and an investment function. Firstly, the existence and uniqueness of the DTFOM solution are proven. Then, some conditions are presented to guarantee that the positive equilibrium point of DTFOM is locally stable. In addition, Hopf bifurcation is obtained by a new method, where the time delay is regarded as the bifurcation parameter. Finally, a numerical example of DTFOM is given to verify the effectiveness of the proposed model and methods.
topic business cycle model
stability
time delay
time-fractional-order
Hopf bifurcation
url https://www.mdpi.com/2227-7390/7/9/846
work_keys_str_mv AT yingkangxie stabilityandbifurcationofadelayedtimefractionalorderbusinesscyclemodelwithageneralliquiditypreferencefunctionandinvestmentfunction
AT zhenwang stabilityandbifurcationofadelayedtimefractionalorderbusinesscyclemodelwithageneralliquiditypreferencefunctionandinvestmentfunction
AT bomeng stabilityandbifurcationofadelayedtimefractionalorderbusinesscyclemodelwithageneralliquiditypreferencefunctionandinvestmentfunction
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