LettersNo Access

IMPULSIVE SYNCHRONIZATION FOR A NEW CHAOTIC OSCILLATOR

SINUHÉ BENÍTEZ

CITEDI-IPN (Mexican Research Center of IPN), 2498 Roll Dr. # 757 Otay Mesa, San Diego, CA 92154, USA

Search for more papers by this author

and

LEONARDO ACHO

CITEDI-IPN (Mexican Research Center of IPN), 2498 Roll Dr. # 757 Otay Mesa, San Diego, CA 92154, USA

Search for more papers by this author

https://doi.org/10.1142/S0218127407017471Cited by:6 (Source: Crossref)

Abstract

Synchronization for a new proposed chaotic system based on impulsive control theory is presented. This new chaotic oscillator is a third order polynomial system (Jerk system), which was developed after the addition of a third state and innovation terms to the well known second order Van der Pol oscillator. The chaotic behavior of this new system is confirmed by using Lyapunov exponents, Poincaré maps, Fourier spectrum analysis and numerical experiments. Impulsive synchronization is achieved using just one channel of communication.

Keywords:

References

L. Acho, J. Rolon and S. Benitez, WSEAS Trans. Circuits Syst. 3, 198 (2004). Google Scholar
Y. Ashkenazy, C. Goren and P. Horwits, Phys. Lett. A 243, 195 (1998), DOI: 10.1016/S0375-9601(98)00240-0. Crossref, Web of Science, Google Scholar
J. C. Chedjouet al., IEEE Trans. Circuit Syst.-I 48, 748 (2001), DOI: 10.1109/81.928157. Crossref, Web of Science, Google Scholar
G. Chen, Control and anticontrol of chaos, Proc. First Int. Conf. Control of Oscillations and Chaos, COC'97 (1997) pp. 181–186, DOI: 10.1109/COC.1997.631323. Google Scholar
G. Chen and T. Ueta, Int. J. Bifurcation and Chaos 9, 1465 (1999), DOI: 10.1142/S0218127499001024. Link, Web of Science, Google Scholar
M. Chen and Z. Han, IEEE Circuits and Syst. Soc. Newsletter 1 (1998). Google Scholar
M. Chen and Z. Han, Int. J. Bifurcation and Chaos 12, 1173 (2002), DOI: 10.1142/S0218127402004991. Link, Web of Science, Google Scholar
A. S. Elwakil, S. Ozoguz and M. P. Kennedy, IEEE Trans. Circuits Syst.-I 49, 527 (2002), DOI: 10.1109/81.995671. Crossref, Web of Science, Google Scholar
Govorukhin, D. N. [2004] http://kvm.math.rsu.ru/matds/ . Google Scholar
J. Guckenheimer, K. Hoffman and W. Weckesser, SIAM J. Appl. Dyn. Syst. 2, 1 (2003), DOI: 10.1137/S1111111102404738. Crossref, Web of Science, Google Scholar
A. Khadra, X. Liu and X. Shen, IEEE Trans. Circuits Syst.-I 50, 341 (2003), DOI: 10.1109/TCSI.2003.808839. Crossref, Web of Science, Google Scholar
H. Khalil , Nonlinear Systems ( Prentice Hall , 2002 ) . Google Scholar
Z. G. Liet al., IEEE Trans. Circuits Syst.-I 48, 1351 (2001), DOI: 10.1109/81.964427. Crossref, Web of Science, Google Scholar
B. Liuet al., IEEE Trans. Circuits Syst.-I 52, 1431 (2005), DOI: 10.1109/TCSI.2005.851708. Web of Science, Google Scholar
D. W. Moore and E. A. Spiegel, Astrophys. J. 143, 871 (1966), DOI: 10.1086/148562. Crossref, Web of Science, Google Scholar
S. Nakagawa and T. Saito, IEEE Trans. Circuits Syst.-I 43, 1019 (1996), DOI: 10.1109/ISCAS.1996.541526. Crossref, Web of Science, Google Scholar
A. I. Panas, T. Yang and L. O. Chua, Int. J. Bifurcation and Chaos 8, 639 (1998), DOI: 10.1142/S0218127498000437. Link, Web of Science, Google Scholar
J. C. Sprott, Phys. Lett. A 266, 19 (2000), DOI: 10.1016/S0375-9601(00)00026-8. Crossref, Web of Science, Google Scholar
J. C. Sprott, Am. J. Phys. 68, 758 (2000), DOI: 10.1119/1.19538. Crossref, Web of Science, Google Scholar
J. C. Sprott and S. J. Linz, Int. J. Chaos Th. Appl. 5, 1 (2000). Google Scholar
J. Sun, Y. Zhang and Q. Wu, Phys. Lett. A 298, 153 (2002), DOI: 10.1016/S0375-9601(02)00466-8. Crossref, Web of Science, Google Scholar
J. J. Thomsen , Vibrations and Stability: Advanced Theory, Analysis, and Tools ( Springer , 2003 ) . Crossref, Google Scholar
X.-F. Wang and G. Chen, IEEE Trans. Circuits Syst.-I 47, 410 (2000), DOI: 10.1109/81.841926. Crossref, Web of Science, Google Scholar
X.-F. Wang, G. Chen and X. Yu, Amer. Instit. Phys. 10, 771 (2000). Google Scholar
T. Yang and L. O. Chua, IEEE Trans. Circuits Syst.-I 44, 976 (1997), DOI: 10.1109/81.633887. Crossref, Web of Science, Google Scholar
T. Yang, IEEE Trans. Atomat. Contr. 44, 1081 (1999), DOI: 10.1109/9.763234. Crossref, Web of Science, Google Scholar