Control of Hopf Bifurcation in Autonomous System Based on Washout Filter
In order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium E0 undergoes a controllable Hopf b...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/482351 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849395495979450368 |
|---|---|
| author | Wenju Du Yandong Chu Jiangang Zhang Yingxiang Chang Jianning Yu Xinlei An |
| author_facet | Wenju Du Yandong Chu Jiangang Zhang Yingxiang Chang Jianning Yu Xinlei An |
| author_sort | Wenju Du |
| collection | DOAJ |
| description | In order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium E0 undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibrium E+. Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems. |
| format | Article |
| id | doaj-art-a7781859ed614aff875d039fadddd4e1 |
| 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-a7781859ed614aff875d039fadddd4e12025-08-20T03:39:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/482351482351Control of Hopf Bifurcation in Autonomous System Based on Washout FilterWenju Du0Yandong Chu1Jiangang Zhang2Yingxiang Chang3Jianning Yu4Xinlei An5Department of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, ChinaIn order to further understand a Lorenz-like system, we study the stability of the equilibrium points and the existence of Hopf bifurcation by center manifold theorem and normal form theory. More precisely, we designed a washout controller such that the equilibrium E0 undergoes a controllable Hopf bifurcation, and by adjusting the controller parameters, we delayed Hopf bifurcation phenomenon of the equilibrium E+. Besides, numerical simulation is given to illustrate the theoretical analysis. Finally, two possible electronic circuits are given to realize the uncontrolled and the controlled systems.http://dx.doi.org/10.1155/2013/482351 |
| spellingShingle | Wenju Du Yandong Chu Jiangang Zhang Yingxiang Chang Jianning Yu Xinlei An Control of Hopf Bifurcation in Autonomous System Based on Washout Filter Journal of Applied Mathematics |
| title | Control of Hopf Bifurcation in Autonomous System Based on Washout Filter |
| title_full | Control of Hopf Bifurcation in Autonomous System Based on Washout Filter |
| title_fullStr | Control of Hopf Bifurcation in Autonomous System Based on Washout Filter |
| title_full_unstemmed | Control of Hopf Bifurcation in Autonomous System Based on Washout Filter |
| title_short | Control of Hopf Bifurcation in Autonomous System Based on Washout Filter |
| title_sort | control of hopf bifurcation in autonomous system based on washout filter |
| url | http://dx.doi.org/10.1155/2013/482351 |
| work_keys_str_mv | AT wenjudu controlofhopfbifurcationinautonomoussystembasedonwashoutfilter AT yandongchu controlofhopfbifurcationinautonomoussystembasedonwashoutfilter AT jiangangzhang controlofhopfbifurcationinautonomoussystembasedonwashoutfilter AT yingxiangchang controlofhopfbifurcationinautonomoussystembasedonwashoutfilter AT jianningyu controlofhopfbifurcationinautonomoussystembasedonwashoutfilter AT xinleian controlofhopfbifurcationinautonomoussystembasedonwashoutfilter |