Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos
A kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/316390 |
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| _version_ | 1849467887630155776 |
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| author | Rongyan Zhang |
| author_facet | Rongyan Zhang |
| author_sort | Rongyan Zhang |
| collection | DOAJ |
| description | A kind of nonlinear finance system with time-delayed feedback is considered.
Firstly, by employing the polynomial theorem to analyze the distribution
of the roots to the associate characteristic equation, the conditions
of ensuring the existence of Hopf bifurcation are given. Secondly, by using
the normal form theory and center manifold argument, we derive the explicit
formulas determining the stability, direction, and other properties of bifurcating
periodic solutions. Finally, we give several numerical simulations, which
indicate that when the delay passes through certain critical values, chaotic
oscillation is converted into a stable steady state or a stable periodic orbit. |
| format | Article |
| id | doaj-art-e6bd93a4e3394afb908c4eac7c288716 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e6bd93a4e3394afb908c4eac7c2887162025-08-20T03:26:00ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/316390316390Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of ChaosRongyan Zhang0Department of Electronic Information Engineering, Huanghe Science and Technology College, Henan, Zhengzhou 450063, ChinaA kind of nonlinear finance system with time-delayed feedback is considered. Firstly, by employing the polynomial theorem to analyze the distribution of the roots to the associate characteristic equation, the conditions of ensuring the existence of Hopf bifurcation are given. Secondly, by using the normal form theory and center manifold argument, we derive the explicit formulas determining the stability, direction, and other properties of bifurcating periodic solutions. Finally, we give several numerical simulations, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable steady state or a stable periodic orbit.http://dx.doi.org/10.1155/2012/316390 |
| spellingShingle | Rongyan Zhang Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos Journal of Applied Mathematics |
| title | Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos |
| title_full | Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos |
| title_fullStr | Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos |
| title_full_unstemmed | Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos |
| title_short | Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos |
| title_sort | bifurcation analysis for a kind of nonlinear finance system with delayed feedback and its application to control of chaos |
| url | http://dx.doi.org/10.1155/2012/316390 |
| work_keys_str_mv | AT rongyanzhang bifurcationanalysisforakindofnonlinearfinancesystemwithdelayedfeedbackanditsapplicationtocontrolofchaos |