Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback
We consider a complex autonomously driven single limit cycle oscillator with delayed feedback. The original model is translated to a two-dimensional system. Through a nonstandard finite-difference (NSFD) scheme we study the dynamics of this resulting system. The stability of the equilibrium of the...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/912374 |
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| _version_ | 1849398433324990464 |
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| author | Yuanyuan Wang Xiaohua Ding |
| author_facet | Yuanyuan Wang Xiaohua Ding |
| author_sort | Yuanyuan Wang |
| collection | DOAJ |
| description | We consider a complex autonomously driven single limit cycle oscillator with delayed feedback.
The original model is translated to a two-dimensional system. Through a nonstandard finite-difference (NSFD) scheme
we study the dynamics of this resulting system. The stability of the equilibrium of the model is investigated
by analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on the
time delay and Hopf bifurcation when the delay passes a sequence of critical
values. Finally, computer simulations are performed to illustrate the
theoretical results. And the results show that NSFD scheme is better than the Euler method. |
| format | Article |
| id | doaj-art-a1f339f7a8cb43989cdafd8416b94b13 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a1f339f7a8cb43989cdafd8416b94b132025-08-20T03:38:35ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/912374912374Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed FeedbackYuanyuan Wang0Xiaohua Ding1Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, ChinaWe consider a complex autonomously driven single limit cycle oscillator with delayed feedback. The original model is translated to a two-dimensional system. Through a nonstandard finite-difference (NSFD) scheme we study the dynamics of this resulting system. The stability of the equilibrium of the model is investigated by analyzing the characteristic equation. In the two-dimensional discrete model, we find that there are stability switches on the time delay and Hopf bifurcation when the delay passes a sequence of critical values. Finally, computer simulations are performed to illustrate the theoretical results. And the results show that NSFD scheme is better than the Euler method.http://dx.doi.org/10.1155/2013/912374 |
| spellingShingle | Yuanyuan Wang Xiaohua Ding Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback Journal of Applied Mathematics |
| title | Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback |
| title_full | Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback |
| title_fullStr | Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback |
| title_full_unstemmed | Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback |
| title_short | Dynamics of a Nonstandard Finite-Difference Scheme for a Limit Cycle Oscillator with Delayed Feedback |
| title_sort | dynamics of a nonstandard finite difference scheme for a limit cycle oscillator with delayed feedback |
| url | http://dx.doi.org/10.1155/2013/912374 |
| work_keys_str_mv | AT yuanyuanwang dynamicsofanonstandardfinitedifferenceschemeforalimitcycleoscillatorwithdelayedfeedback AT xiaohuading dynamicsofanonstandardfinitedifferenceschemeforalimitcycleoscillatorwithdelayedfeedback |