Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller
Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and ra...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/2028037 |
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| _version_ | 1832550806671327232 |
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| author | Jie Ran Yanmin Liu Jun He Xiang Li |
| author_facet | Jie Ran Yanmin Liu Jun He Xiang Li |
| author_sort | Jie Ran |
| collection | DOAJ |
| description | Based on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and random feedback control can be faster than those of dislocated and ordinary feedback control. The random feedback control method, which does not require any adjustable control parameters of the model, just only slightly changes the random intensity. Finally, numerical simulations are presented to verify the effectiveness of the proposed controllers. |
| format | Article |
| id | doaj-art-e83a82dff63a4c3280e4a1a28116078c |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e83a82dff63a4c3280e4a1a28116078c2025-02-03T06:05:46ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/20280372028037Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback ControllerJie Ran0Yanmin Liu1Jun He2Xiang Li3School of Mathematics and Computer Science, Zunyi Normal College, Zunyi 563002, ChinaSchool of Mathematics and Computer Science, Zunyi Normal College, Zunyi 563002, ChinaSchool of Mathematics and Computer Science, Zunyi Normal College, Zunyi 563002, ChinaSchool of Mathematics and Computer Science, Zunyi Normal College, Zunyi 563002, ChinaBased on the stability and orthogonal polynomial approximation theory, the ordinary, dislocated, enhancing, and random feedback control methods are used to suppress the Neimark-Sacker bifurcation to fixed point in this paper. It is shown that the convergence rate of enhancing feedback control and random feedback control can be faster than those of dislocated and ordinary feedback control. The random feedback control method, which does not require any adjustable control parameters of the model, just only slightly changes the random intensity. Finally, numerical simulations are presented to verify the effectiveness of the proposed controllers.http://dx.doi.org/10.1155/2016/2028037 |
| spellingShingle | Jie Ran Yanmin Liu Jun He Xiang Li Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller Advances in Mathematical Physics |
| title | Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller |
| title_full | Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller |
| title_fullStr | Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller |
| title_full_unstemmed | Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller |
| title_short | Controlling Neimark-Sacker Bifurcation in Delayed Species Model Using Feedback Controller |
| title_sort | controlling neimark sacker bifurcation in delayed species model using feedback controller |
| url | http://dx.doi.org/10.1155/2016/2028037 |
| work_keys_str_mv | AT jieran controllingneimarksackerbifurcationindelayedspeciesmodelusingfeedbackcontroller AT yanminliu controllingneimarksackerbifurcationindelayedspeciesmodelusingfeedbackcontroller AT junhe controllingneimarksackerbifurcationindelayedspeciesmodelusingfeedbackcontroller AT xiangli controllingneimarksackerbifurcationindelayedspeciesmodelusingfeedbackcontroller |