Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect
The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Ho...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/1263602 |
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| _version_ | 1832559948845809664 |
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| author | Wenjie Hu Hua Zhao Tao Dong |
| author_facet | Wenjie Hu Hua Zhao Tao Dong |
| author_sort | Wenjie Hu |
| collection | DOAJ |
| description | The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear. |
| format | Article |
| id | doaj-art-08bc8d8664a54ac0a05aad80ca63dba0 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-08bc8d8664a54ac0a05aad80ca63dba02025-02-03T01:28:39ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/12636021263602Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion EffectWenjie Hu0Hua Zhao1Tao Dong2College of Economics and Business Administration, Chongqing University, Chongqing 400030, ChinaCollege of Economics and Business Administration, Chongqing University, Chongqing 400030, ChinaCollege of Electronics and Information Engineering, Southwest University, Chongqing 400715, ChinaThe dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear.http://dx.doi.org/10.1155/2018/1263602 |
| spellingShingle | Wenjie Hu Hua Zhao Tao Dong Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect Complexity |
| title | Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect |
| title_full | Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect |
| title_fullStr | Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect |
| title_full_unstemmed | Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect |
| title_short | Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect |
| title_sort | dynamic analysis for a kaldor kalecki model of business cycle with time delay and diffusion effect |
| url | http://dx.doi.org/10.1155/2018/1263602 |
| work_keys_str_mv | AT wenjiehu dynamicanalysisforakaldorkaleckimodelofbusinesscyclewithtimedelayanddiffusioneffect AT huazhao dynamicanalysisforakaldorkaleckimodelofbusinesscyclewithtimedelayanddiffusioneffect AT taodong dynamicanalysisforakaldorkaleckimodelofbusinesscyclewithtimedelayanddiffusioneffect |