Hopf Bifurcation and Chaos of a Delayed Finance System
In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf b...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6715036 |
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| _version_ | 1832559156851113984 |
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| author | Xuebing Zhang Honglan Zhu |
| author_facet | Xuebing Zhang Honglan Zhu |
| author_sort | Xuebing Zhang |
| collection | DOAJ |
| description | In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state. |
| format | Article |
| id | doaj-art-955bb55b823248699f97a52d018249db |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-955bb55b823248699f97a52d018249db2025-02-03T01:30:46ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/67150366715036Hopf Bifurcation and Chaos of a Delayed Finance SystemXuebing Zhang0Honglan Zhu1College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, ChinaBusiness School, Huaiyin Institute of Technology, Huaian, ChinaIn this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.http://dx.doi.org/10.1155/2019/6715036 |
| spellingShingle | Xuebing Zhang Honglan Zhu Hopf Bifurcation and Chaos of a Delayed Finance System Complexity |
| title | Hopf Bifurcation and Chaos of a Delayed Finance System |
| title_full | Hopf Bifurcation and Chaos of a Delayed Finance System |
| title_fullStr | Hopf Bifurcation and Chaos of a Delayed Finance System |
| title_full_unstemmed | Hopf Bifurcation and Chaos of a Delayed Finance System |
| title_short | Hopf Bifurcation and Chaos of a Delayed Finance System |
| title_sort | hopf bifurcation and chaos of a delayed finance system |
| url | http://dx.doi.org/10.1155/2019/6715036 |
| work_keys_str_mv | AT xuebingzhang hopfbifurcationandchaosofadelayedfinancesystem AT honglanzhu hopfbifurcationandchaosofadelayedfinancesystem |