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CHAOS AND ROBUST ADAPTIVE SYNCHRONIZATION IN A NONLINEAR EMITTER–RECEIVER SYSTEM

Laboratory of Research in Advanced Material and Nonlinear Sciences, Department of Physics, Faculty of Science, University of Buea, P. O. Box 63 Buea, Cameroon

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SAMUEL BOWONG

Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P. O. Box 24157 Douala, Cameroon

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https://doi.org/10.1142/S0218127407019007Cited by:1 (Source: Crossref)

Abstract

This work studies transitions to chaos and adaptive synchronization of a nonlinear emitter–receiver system in a drive–response framework. Safe bifurcations and explosive bifurcations are observed. A robust adaptive observer-based response system is designed to synchronize the emitter–receiver system with unknown parameters and external disturbances. Lyapunov stability ensures global synchronization between the drive and response systems even if Lipschitz constants on functions matrices and bound on uncertainties are unknown. Computer simulations are provided to illustrate the designed adaptive synchronization scheme.

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References

S. Bowong, F. M. Moukam Kakmeni and R. Koina, Int. J. Bifurcation and Chaos 14, 2477 (2004). Link, Web of Science, Google Scholar
G. Chen, Phys. Scripta 68, 326 (1994). Web of Science, Google Scholar
G. Chen and X. Dong , From Chaos to Order: Methodologies, Perspectives and Applications ( World Scientific , Singapore , 1998 ) . Link, Google Scholar
L. O. Chuaet al., Int. J. Bifurcation and Chaos 2, 705 (1992). Link, Web of Science, Google Scholar
R. Femat and G. Solis-Perales, Phys. Lett. A 262, 50 (1999), DOI: 10.1016/S0375-9601(99)00667-2. Crossref, Web of Science, Google Scholar
C. Grebogi, E. Ott and J. A. G. York, Physica D 7, 181 (1983), DOI: 10.1016/0167-2789(83)90126-4. Crossref, Web of Science, Google Scholar
S. Hayes, C. Grebogi and E. Ott, Phys. Rev. Lett. 70, 3031 (1993), DOI: 10.1103/PhysRevLett.70.3031. Crossref, Web of Science, Google Scholar
S. Hayeset al., Phys. Rev. Lett. 73, 1781 (1994), DOI: 10.1103/PhysRevLett.73.1781. Crossref, Web of Science, Google Scholar
T. Kapitaniak , Controlling Chaos ( Academic Press , London , 1996 ) . Google Scholar
T. Kapitaniak, M. Sekeita and M. Ogorzalek, Int. J. Bifurcation and Chaos 6, 211 (1996). Link, Web of Science, Google Scholar
M. Lakshamanam and K. Murali , Chaos in Nonlinear Oscillators, Controlling and Synchronization ( World Scientific , Singapore , 1996 ) . Crossref, Google Scholar
T. L. Liao and H. S. Huang, IEEE Trans. Circuits Syst.-I 4, 1144 (1999). Google Scholar
J. Lu, G. Chen and S. Zhang, Int. J. Bifurcation and Chaos 5, 1001 (2002). Google Scholar
R. Marino and P. Tomei , Nonlinear Control Design-Geometric, Adaptive, Robust ( Prentice-Hall , Englewood Cliffs, NJ , 1995 ) . Google Scholar
O. Morgül and E. Solak, Phys. Rev. E 54, 4803 (1996). Crossref, Web of Science, Google Scholar
O. Morgül and E. Solak, Int. J. Bifurcation and Chaos 7, 1307 (1997). Link, Web of Science, Google Scholar
F. M. Moukam Kakmeniet al., Physica A 333, 87 (2004). Crossref, Web of Science, Google Scholar
F. M. Moukam Kakmeniet al., Chaos Solit. Fract. 21, 1093 (2004). Crossref, Web of Science, Google Scholar
A. Nath and D. S. Ray, Phys. Rev. A 34, 4472 (1986), DOI: 10.1103/PhysRevA.34.4472. Crossref, Web of Science, Google Scholar
H. Nijmeijer and I. M. Y. Mareels, IEEE Trans. Circuits Syst.-I 7, 882 (1997). Web of Science, Google Scholar
M. J. Ogarzalek, IEEE Trans. Circuits Syst.-I 40, 693 (1993). Crossref, Web of Science, Google Scholar
A. G. Oliviera and A. J. Jones, Int. J. Bifurcation and Chaos 8, 2225 (1998). Link, Web of Science, Google Scholar
L. Pecora and T. S. Carroll, Phys. Rev. Lett. 64, 821 (1990), DOI: 10.1103/PhysRevLett.64.821. Crossref, Web of Science, Google Scholar
L. Pecoraet al., Int. J. Bifurcation and Chaos 2, 273 (2000). Link, Web of Science, Google Scholar
A. Pikovsky , M. Rosenblum and J. Kurths , Synchronization: A Universal Concept in Nonlinear Sciences ( Cambridge University Press , 2001 ) . Crossref, Google Scholar
K. Pyragas, Phys. Lett. A 170, 421 (1992), DOI: 10.1016/0375-9601(92)90745-8. Crossref, Web of Science, Google Scholar
E. Rosa, S. Hayes and C. Grebogi, Phys. Rev. Lett. 78, 1247 (1997), DOI: 10.1103/PhysRevLett.78.1247. Crossref, Web of Science, Google Scholar
G. Santoboni, A. Y. Pogromsky and H. Nijmeiher, Phys. Lett. A 291, 267 (2001), DOI: 10.1016/S0375-9601(01)00652-1. Web of Science, Google Scholar
G. Solis-Perales, R. Fermat and E. Ruiz–Velazquez, Phys. Lett. A 288, 183 (2001), DOI: 10.1016/S0375-9601(01)00545-X. Crossref, Web of Science, Google Scholar
J. M. T. Thompson, H. B. Stewart and Y. Veda, Phys. Rev. E 49, 1019 (1994), DOI: 10.1103/PhysRevE.49.1019. Crossref, Web of Science, Google Scholar
P. Woafo, Phys. Rev. A 267, 31 (2000). Google Scholar