Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays
The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by con...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/686274 |
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| _version_ | 1850160726890512384 |
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| author | Yanhui Zhai Ying Xiong Xiaona Ma |
| author_facet | Yanhui Zhai Ying Xiong Xiaona Ma |
| author_sort | Yanhui Zhai |
| collection | DOAJ |
| description | The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid. |
| format | Article |
| id | doaj-art-a4a08cf401264fa3ab3317dbba07be11 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a4a08cf401264fa3ab3317dbba07be112025-08-20T02:23:05ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/686274686274Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two DelaysYanhui Zhai0Ying Xiong1Xiaona Ma2School of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaSchool of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaThe paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid.http://dx.doi.org/10.1155/2014/686274 |
| spellingShingle | Yanhui Zhai Ying Xiong Xiaona Ma Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays Abstract and Applied Analysis |
| title | Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays |
| title_full | Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays |
| title_fullStr | Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays |
| title_full_unstemmed | Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays |
| title_short | Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays |
| title_sort | hopf bifurcation analysis in a modified price differential equation model with two delays |
| url | http://dx.doi.org/10.1155/2014/686274 |
| work_keys_str_mv | AT yanhuizhai hopfbifurcationanalysisinamodifiedpricedifferentialequationmodelwithtwodelays AT yingxiong hopfbifurcationanalysisinamodifiedpricedifferentialequationmodelwithtwodelays AT xiaonama hopfbifurcationanalysisinamodifiedpricedifferentialequationmodelwithtwodelays |