Current issue
Archive
About the Journal
Editorial Policies
For Authors
3/2013 vol. 18
Stats
Get citation
ORIGINAL PAPER
Projective Synchronization of Chaotic Systems Via Backstepping Design
A. Tarai 1
,
 
M.A. Khan 2
 
 
 
More details
Hide details
1
Department of Mathematics, Aligunj R.R.B. High School Midnapore (West), West Bengal, INDIA
 
2
Department of Mathematics, Garhbeta Ramsundar Vidyabhavan Garhbeta, Midnapore (West), West Bengal, INDIA
 
 
Online publication date: 2013-09-06
 
 
Publication date: 2013-08-01
 
 
International Journal of Applied Mechanics and Engineering 2013;18(3):965-973
DOI: https://doi.org/10.2478/ijame-2013-0060
 
 
Article (PDF)
References (18)
 
KEYWORDS
Lyapunov function
projective synchronization
backstepping
design
 
ABSTRACT
Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm
 
REFERENCES (18)
1.
Blasius, Huppert and Stone (1999): Complex dynamics and phase synchronization in spatially extended ecological systems. - Nature, pp.399.
Google Scholar
 
 
2.
Gonzalez-Miranda J.M. (1998): Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving. - Phys. Rev.E., vol.57, p.7321.
Google Scholar
 
 
3.
Hayes, Grebogi and Ott (1993): Communicating with chaos. - Phys. Rev. Lett., vol.70, pp.30-31.
Google Scholar
 
 
4.
Khan M.A. and Mandal A.K. (2009): Generalized chaos synchronization of coupled Rossler system. - Bull. Cal. Math. Soc. vol.101, No.2, pp.197-204.
Google Scholar
 
 
5.
Khan M.A., Mandal A.K. and Poria S. (2011): Three control strategy for unified chaotic system. - Int. J. of Applied Mechanics and Engineering, vol.16, No.2, pp.597-608.
Google Scholar
 
 
6.
Khan M.A., Pal S.N. and Poria S. (2012): Generalized anti-synchronization of different chaotic systems. - Int. J. of Applied Mechanics and Engineering , vol.17, No.1, pp.83-89.
Google Scholar
 
 
7.
Laoye, Vincent and Kareem (2009): Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller. - Chaos, Solitons and Fractals, vol.39, No.1, pp.356-362.
Google Scholar
 
 
8.
Mainieri R. and Rehacek J. (1999): Projective synchronization in three-dimensional chaotic system. - Phys. Rev. Lett. vol.82, No.15, p.3042.
Google Scholar
 
 
9.
Parlitz, Junge and Kocarev (1996): Synchronization-based parameter estimation from time series. - Phys. Rev. E., vol.54, pp.62-53.
Google Scholar
 
 
10.
Pecora and Carroll (1990): Synchronization in chaotic systems. - Phy. Rev. Lett., vol.64, No.8, pp.821-824.
Google Scholar
 
 
11.
Poria S. (2007): The linear generalized chaos synchronization and predictability. - Int. J. of Applied Mechanics and Engineering , vol.12, No.3, pp.879-885.
Google Scholar
 
 
12.
Rosenblum M., Pikovosky A. and Kurths J. (1996): Phase synchronization of chaotic oscillators. - Phys. Rev. Lett., vol.76, p.1804.
Google Scholar
 
 
13.
Rulkov N.F., Suschik M.M. and Tsimring L.S. (1995): Generalized synchronization of chaos in directionally coupled chaotic systems. - Phys. Rev.E., vol.51, p.980.
Google Scholar
 
 
14.
Tan, Zhang and Yang (2003): Synchronizing chaotic systems using backstepping design. - Chaos, Solitons and Fractals, vol.16, pp.37.
Google Scholar
 
 
15.
Tarai A., Poria S. and Chatterjee P. (2009): Synchronization of bi-directionally coupled chaotic Chen’s system with delay - Chaos, Solitons and Fractals, vol.40, pp.885-892.
Google Scholar
 
 
16.
Tarai A., Poria S. and Chatterjee P. (2007): Synchronization of bi-directionally coupled chaotic Chen’s system with delay - Chaos, Solitons and Fractals, doi.10.1016/j.chaos 2007.11.025.
Google Scholar
 
 
17.
Wang C. and Ge S.S. (2001): Adaptive synchronization of uncertain chaotic systems via backstepping design. - Chaos, Solitons and Fractals, vol.12, pp.1199-1206.
Google Scholar
 
 
18.
Yongguang Y. and Suochun Z. (2003): Controlling uncertain Lu system using backstepping design. - Chaos, Solitons and Fractals, vol.15, pp.897-902.
Google Scholar
 
 
Share
Send by email
RELATED ARTICLE
Design With SADSF Method and Analyses of Elastic Properties of Torsion-Loaded Double-Tee Section With Torsional Box
Indexes
 
Keywords index
Topics index
Authors index
eISSN:2353-9003
ISSN:1734-4492
Journals System - logo
In the years 2019-2020, the International Journal of Applied Mechanics and Engineering is financed under contract no. 634/P-DUN/2019 by the Minister of Science and Higher Education from funds for science dissemination activities. The financing amounts to 83.500 PLN.
Task: edition of a scientific journal, its internationalization and ensuring open access to the journal via the Internet
© 2006-2024 Journal hosting platform by Bentus
Scroll to top