| Title:
|
Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers (English) |
| Author:
|
Zhang, Lan |
| Author:
|
Zhang, Chengjian |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
35-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences between the analysis of the hyperchaotic Lorenz system, hyperchaotic Chen system and hyperchaotic Lü system. (English) |
| Keyword:
|
Hopf bifurcation |
| Keyword:
|
periodic solution |
| Keyword:
|
multiple delays and parameters |
| Keyword:
|
hyperchaotic Lü system |
| Keyword:
|
hyperchaotic Chen system |
| Keyword:
|
hyperchaotic Lorenz system |
| MSC:
|
34K18 |
| MSC:
|
37D45 |
| MSC:
|
37N35 |
| MSC:
|
93C15 |
| idZBL:
|
Zbl 1145.93361 |
| idMR:
|
MR2405053 |
| . |
| Date available:
|
2009-09-24T20:31:47Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135831 |
| . |
| Reference:
|
[1] Chen A. M., Lu J. A., Lü J. H., Yu S. M.: Generating hyperchaotic Lü attractor via state feedback control.Physica A 364 (2006), 103–110 |
| Reference:
|
[2] Wolf A., Swift J. B., Swinney H. L., Vastano J. A.: Determining Lyapunov exponents from a time series.Physica D 16 (1985), 285–317 Zbl 0585.58037, MR 0805706 |
| Reference:
|
[3] Wei J. J., Ruan S. G.: Stability and bifurcation in a neural network model with two delays.Physica D 130 (1999), 255–272 Zbl 1066.34511, MR 1692866 |
| Reference:
|
[4] Briggs K.: An improved method for estimating Liapunov exponents of chaotic time series.Phys. Lett. A 151 (1990), 27–32 MR 1085170 |
| Reference:
|
[5] Cooke K. L., Grossman Z.: Discrete delay, distribute delay and stability switches.J. Math. Anal. Appl. 86 (1982), 592–627 MR 0652197 |
| Reference:
|
[6] Olien L., Belair J.: Bifurcation, stability and monotonicity properities of a delayed neural network model.Physica D 102 (1997), 349–363 MR 1439692 |
| Reference:
|
[7] Heyes N. D.: Linear autonomous neutral functional differential equations.J. Differential Equations 15 (1974), 106–128 MR 0338520 |
| Reference:
|
[8] Jia Q.: Hyperchaos generated from the Lorenz chaotic system and its control.Phys. Lett. A 366 (2007), 217–222 Zbl 1203.93086 |
| Reference:
|
[9] Datko R.: A procedure for determination of the exponential stability of certain differential difference equations.Quart. Appl. Math. 36 (1978), 279–292 Zbl 0405.34051, MR 0508772 |
| Reference:
|
[10] Wu X. J.: Chaos synchronization of the new hyperchaotic Chen system via nonlinear control.Acta Phys. Sinica 22 (2006), 12, 6261–6266 |
| . |
