ABSTRACT
This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. Numerical results are presented to check the effectiveness of the proposed synchronization scheme. The results suggest that the linear and nonlinear terms in the feedback coupling play a complementary role in increasing the synchronization regime in the parameter space of the synchronization manifold. The proposed method can be successfully applied to a large variety of physical systems.
ACKNOWLEDGMENTS
F.M.M.K. thanks the PIK-Potsdam (Germany) for the partial support of this research. S.B. and D.V.S. acknowledge the support by the Alexander von Humboldt Foundation. F.M.M.K. would also like to acknowledge the partial financial support of the ICTP in Trieste-Italy under the Associate Federation Scheme. D.V.S. and J.K. acknowledge the support from EU Project No. 240763 PHOCUS(FP7-ICT-2009-C).
- 1. A. Pikovsky, M. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001). Google ScholarCrossref
- 2. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. Zhou, Phys. Rep. 366, 1 (2002). https://doi.org/10.1016/S0370-1573(02)00137-0, Google ScholarCrossref
- 3. P. So, B. C. Cotton, and E. Barreto, Chaos 18, 037114 (2008). https://doi.org/10.1063/1.2979693, Google ScholarScitation
- 4. A. Koseska, E. Volkov, and J. Kurths, Chaos 20, 023132 (2010). https://doi.org/10.1063/1.3456937, Google ScholarScitation
- 5. H. Ulrichs, A. Mann, and U. Parlitz, Chaos 19, 043120 (2009). https://doi.org/10.1063/1.3266924, Google ScholarScitation
- 6. Y. Sun and J. Ruan, Chaos 19, 043113 (2009). https://doi.org/10.1063/1.3262488, Google ScholarScitation
- 7. F. Sorrentino, G. Barlev, A. B. Cohen, and E. Ott, Chaos 20, 013103 (2010). https://doi.org/10.1063/1.3279646, Google ScholarScitation
- 8. S. Bowong and F. M. Moukam Kakmeni, Phys. Lett. A 316, 206 (2003). https://doi.org/10.1016/S0375-9601(03)01152-6, Google ScholarCrossref
- 9. F. M. Moukam Kakmeni, S. Bowong, C. Tchawoua, and E. Kaptouom, Phys. Lett. A 322, 305 (2004). https://doi.org/10.1016/j.physleta.2004.01.016, Google ScholarCrossref
- 10. L. Wang, H. P. Dai, H. Dong, Y. Y. Cao, and Y. X. Sun, Eur. Phys. J. B 61, 335 (2008). https://doi.org/10.1140/epjb/e2008-00081-5, Google ScholarCrossref
- 11. V. Volterra, Leçons sur la Théorie Mathématique de la Lutte Pour la Vie (Gauthiers-Villars, Paris, 1931). Google Scholar
- 12. F. Ghiringhelli and M. N. Zervas, Phys. Rev. E 65, 036604 (2002) https://doi.org/10.1103/PhysRevE.65.036604; Google ScholarCrossref
F. M. Atay, Phys. Rev. Lett. 91, 094101 (2003). https://doi.org/10.1103/PhysRevLett.91.094101, , Google ScholarCrossref - 13. H. K. Khalil, Nonlinear Systems, 3rd ed. (Springer-Verlag, London, 1995). Google Scholar
- 14. D. V. Senthilkumar, M. Lakshmanan, and J. Kurths, Phys. Rev. E 74, 035205(R) (2006). https://doi.org/10.1103/PhysRevE.74.035205, Google ScholarCrossref
- 15. D. V. Senthilkumar, J. Kurths, and M. Lakshmanan, Phys. Rev. E 79, 066208 (2008). https://doi.org/10.1103/PhysRevE.79.066208, Google ScholarCrossref
- 16. F. M. Moukam Kakmeni, S. Bowong, and C. Tchawoua, Phys. Lett. A 355, 47 (2006). https://doi.org/10.1016/j.physleta.2006.01.103, Google ScholarCrossref
- 17. M. Chen, D. Zhou, and Y. Shang, Phys. Lett. A 337, 384 (2005). https://doi.org/10.1016/j.physleta.2005.02.006, Google ScholarCrossref
- 18. H. N. Pishkenari, N. Jalili, S. H. Mahboobi, A. Alasty, and A. Meghdari, Chaos 20, 023105 (2010). https://doi.org/10.1063/1.3383655, Google ScholarScitation
- 19. M. Dhamala, V. K. Jirsa, and M. Ding, Phys. Rev. Lett. 92, 074104 (2004). https://doi.org/10.1103/PhysRevLett.92.074104, Google ScholarCrossref
- 20. V. M. Popov, Hyperstability of Control System (Springer-Verlag, Berlin, 1973). Google ScholarCrossref
- 21. E. M. Shahverdiev, R. A. Nuriev, R. H. Hashimov, and K. A. Shore, Chaos, Solitons Fractals 25, 325 (2005). https://doi.org/10.1016/j.chaos.2004.08.009, Google ScholarCrossref
- 22. K. Pyragas, Phys. Lett. A 170, 421 (1992). https://doi.org/10.1016/0375-9601(92)90745-8, Google ScholarCrossref
- 23. F. M. Moukam Kakmeni, S. Bowong, L. Nana, and T. C. Kofane, Chaos, Solitons Fractals 39, 248 (2009). https://doi.org/10.1016/j.chaos.2007.01.140, Google ScholarCrossref
- 24. M. A. Trevisan, J. M. Mendez, and G. B. Mindlin, Phys. Rev. E 73, 061911 (2006). https://doi.org/10.1103/PhysRevE.73.061911, Google ScholarCrossref
- 25. T. Gardner, G. Cecchi, M. Magnasco, R. Laje, and G. B. Mindlin, Phys. Rev. Lett. 87, 208101 (2001). https://doi.org/10.1103/PhysRevLett.87.208101, Google ScholarCrossref
- 26. R. Laje, T. J. Gardner, and G. B. Mindlin, Phys. Rev. E 65, 051921 (2002). https://doi.org/10.1103/PhysRevE.65.051921, Google ScholarCrossref
- 27. E. J. Ngamga Ketchamen, L. Nana, and T. C. Kofane, Chaos, Solitons Fractals 20, 1141 (2004). https://doi.org/10.1016/j.chaos.2003.09.040, Google ScholarCrossref
- 28. A. Ahlborn and U. Parlitz, Phys. Rev. Lett. 93, 264101 (2004) https://doi.org/10.1103/PhysRevLett.93.264101; Google ScholarCrossref
A. Ahlborn and U. Parlitz, Phys. Rev. E 75, 065202(R) (2007) https://doi.org/10.1103/PhysRevE.75.065202; , Google ScholarCrossref
A. Ahlborn and U. Parlitz, Opt. Lett. 31, 465 (2006). https://doi.org/10.1364/OL.31.000465, , Google ScholarCrossref
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