Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays
A competitive model of market structure with consumptive delays is considered. The local stability of the positive equilibrium and the existence of local Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equation. The explicit formulas dete...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/852025 |
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| _version_ | 1832549241066618880 |
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| author | Xuhui Li |
| author_facet | Xuhui Li |
| author_sort | Xuhui Li |
| collection | DOAJ |
| description | A competitive model of market structure with consumptive delays is considered. The local stability of the positive equilibrium and the existence of local Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equation. The explicit formulas determining the stability and other properties of bifurcating periodic solutions are derived by using normal form theory and center manifold argument. Finally, numerical simulations are given to support the analytical results. |
| format | Article |
| id | doaj-art-7713a6f692f44f4599ef52d06e0b38d4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7713a6f692f44f4599ef52d06e0b38d42025-02-03T06:11:45ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/852025852025Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive DelaysXuhui Li0Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200030, ChinaA competitive model of market structure with consumptive delays is considered. The local stability of the positive equilibrium and the existence of local Hopf bifurcation are investigated by analyzing the distribution of the roots of the associated characteristic equation. The explicit formulas determining the stability and other properties of bifurcating periodic solutions are derived by using normal form theory and center manifold argument. Finally, numerical simulations are given to support the analytical results.http://dx.doi.org/10.1155/2014/852025 |
| spellingShingle | Xuhui Li Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays Journal of Applied Mathematics |
| title | Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays |
| title_full | Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays |
| title_fullStr | Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays |
| title_full_unstemmed | Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays |
| title_short | Local Hopf Bifurcation in a Competitive Model of Market Structure with Consumptive Delays |
| title_sort | local hopf bifurcation in a competitive model of market structure with consumptive delays |
| url | http://dx.doi.org/10.1155/2014/852025 |
| work_keys_str_mv | AT xuhuili localhopfbifurcationinacompetitivemodelofmarketstructurewithconsumptivedelays |