| GENERAL |
|
|
|
|
Anti-Control of Hopf Bifurcation in the Chaotic Liu System with Symbolic Computation |
| LÜ Zhuo-Sheng1, DUAN Li-Xia2 |
| 1School of Science, Beijing University of Posts and Telecommunications, Beijing 1008762School of Science, North China University of Technology, Beijing |
|
| Cite this article: |
|
LÜ, Zhuo-Sheng, DUAN Li-Xia 2009 Chin. Phys. Lett. 26 050504 |
|
|
|
Abstract The anti-control of bifurcation refers to the task of creating a certain bifurcation with particular desired properties and location by appropriate controls. We consider, via feedback control and symbolic computation, the problem of anti-control of Hopf bifurcation in the chaotic Liu system. We propose an anti-control scheme and show that compared with the uncontrolled system, the anti-controlled Liu system can exhibit Hopf bifurcation in a much larger parameter region. The anti-control strategy used keeps the equilibrium structure of the Liu system and can be applied to generate Hopf bifurcation at the desired location with preferred stability. We illustrate the efficiency of the anti-control approach under different operating
conditions.
|
| Keywords:
05.45.-a
|
|
|
Received: 21 November 2008
Published: 23 April 2009
|
|
| PACS: |
05.45.-a
|
(Nonlinear dynamics and chaos)
|
|
|
|
|
|
[1] Chen G and Ueta T 1999 Int. J. Bifur. Chaos 91465
[2] L\"{u J and Chen G 2002 Int. J. Bifur. Chaos 12 659
[3] Celikovsky S and Chen G 2002 Proceedings of the 15thTriennial World Congress of IFAC (Barcelona, Spain)
[4] Liu C X, Liu T, Liu L and Liu K 2004 Chaos,Solitons Fract. 22 1031
[5] Celikovsky S and Chen G 2005 Chaos, Solitons Fract. 26 1271
[6] Wang F Q and Liu C X 2006 Acta Phys. Sin. 555061 (in Chinese)
[7] Yassen M T 2006 Phys. Lett. A 350 36
[8] Yassen M T 2007 Phys. Lett. A 360 582
[9] Matouk A E 2008 Nonlin. Anal.: TMA 69 3213
[10] Wang F Q and Liu C X 2006 Acta Phys. Sin. 555055 (in Chinese)
[11] Kemih K and Benslama M 2006 Int. J. Inf. Tech. 3 186
[12] Kemih K and Benslama M and Baudrand H 2006 Asian J.Inf. Tech. 5 1301
[13] Titz S, Kuhlbrodt T, Rahmsdorf S and Feudel U 2001 Tellus A 54 89
[14] Chen D S, Wang H O and Chen G 2001 IEEE Trans.Circuits Syst. I: FTA 48 661
[15] Chen Z and Yu P 2005 Chaos, Solitons Fract. 26 1231
[16] Kuznetsov Y A 1998 Elements of Applied BifurcationTheory 2nd edn (New York: Springer) |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
