| Title:
|
A new approach to generalized chaos synchronization based on the stability of the error system (English) |
| Author:
|
Zhu, Zhiliang |
| Author:
|
Li, Shuping |
| Author:
|
Yu, Hai |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
492-500 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity. Further generalization and appropriation can be acquired without a stability requirement for the chaotic system’s linear part. The Lorenz system and a hyperchaotic system are taken for illustration and verification and the results of the simulation indicate that the method is effective. (English) |
| Keyword:
|
chaotic system |
| Keyword:
|
generalized synchronization |
| Keyword:
|
configuration of poles |
| Keyword:
|
synchronous velocity |
| MSC:
|
37N35 |
| MSC:
|
58E25 |
| MSC:
|
93B55 |
| MSC:
|
93C10 |
| idZBL:
|
Zbl 1172.93015 |
| idMR:
|
MR2459067 |
| . |
| Date available:
|
2009-09-24T20:37:01Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135868 |
| . |
| Reference:
|
[1] Carroll L., Pecora M.: Synchronizing chaotic circuits.IEEE Trans. Circuits and Systems 38 (2001), 4, 453–456 Zbl 1058.37538 |
| Reference:
|
[2] Chua L. O.: Experimental chaos synchronization in Chua’s circuit.Internat. J. Bifurc. Chaos 2 (2002), 3, 705–708 Zbl 0875.94133 |
| Reference:
|
[3] Dachselt F., Schwarz W.: Chaos and cryptography.IEEE Trans. Circuits and Systems, Fundamental Theory and Applications 48 (2001), 12, 1498–1509 Zbl 0999.94030, MR 1873100 |
| Reference:
|
[4] Elabbasy E. M., Agiza H. N., El-Dessoky M. M.: Controlling and synchronization of Rossler system with uncertain parameters.Internat. J. Nonlinear Sciences and Numerical Simulation 5 (2005), 2, 171–181 MR 2087956 |
| Reference:
|
[5] Fang J. Q.: Control and synchronization of chaos in nonlinear systems and prospects for application 2.Progr. Physics 16 (1996), 2, 174–176 |
| Reference:
|
[6] Fang J. Q.: Mastering Chaos and Development High-tech.Atomic Energy Press, Beijing, 2002 |
| Reference:
|
[7] Gao Y., Weng J. Q., al. X. S. Luo et: Generalized synchronization of hyperchaotic circuit.J. Electronics 6 (2002), 24. 855–959 |
| Reference:
|
[8] Kapitaniak T.: Experimental synchronization of chaos using continuous control.Internat. J. Bifurc. Chaos 4 (2004), 2, 483–488 Zbl 0825.93298 |
| Reference:
|
[9] Kocarev L., Parlitz U.: Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems.Phys. Rev. Lett. 11 (1996), 76, 1816–1819 |
| Reference:
|
[10] Lorenz E. N.: Deterministic nonperiodic flow.J. Atmospheric Sci. 20 (1963), 1. 130–141 |
| Reference:
|
[11] Pecora M., Carroll L.: Synchronization in chaotic systems.Phys. Rev. Lett. 64 (1990), 8, 821–823 Zbl 0938.37019, MR 1038263 |
| Reference:
|
[12] Pecora M., Carroll L.: Driving systems with chaotic signals.Phys. Rev. A 44 (2001), 4, 2374–2383 |
| Reference:
|
[13] Yang T., Chua L. O.: Generalized synchronization of chaos via linear transformations.Internat. J. Bifur. Chaos 9 (1999), 1, 215–219 Zbl 0937.37019, MR 1689607 |
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