No Access Submitted: 20 July 2013 Accepted: 20 October 2013 Published Online: 06 November 2013
Chaos 23, 043115 (2013); https://doi.org/10.1063/1.4828515
Lag synchronization is a basic phenomenon in mismatched coupled systems, delay coupled systems, and time-delayed systems. It is characterized by a lag configuration that identifies a unique time shift between all pairs of similar state variables of the coupled systems. In this report, an attempt is made how to induce multiple lag configurations in coupled systems when different pairs of state variables attain different time shift. A design of coupling is presented to realize this multiple lag synchronization. Numerical illustration is given using examples of the Rössler system and the slow-fast Hindmarsh-Rose neuron model. The multiple lag scenario is physically realized in an electronic circuit of two Sprott systems.
S.K.B. acknowledges support by the BRNS/DAE, India (Project No. 2009/34/26/BRNS). S.K.D. is supported by the CSIR Emeritus scientist scheme. The authors thank the anonymous reviewer for his great effort in improvisation of the manuscript.
  1. 1. M. Rosenblum, A. S. Pikovsky, and J. Kurths, Phys. Rev. Lett. 78, 4193 (1997); https://doi.org/10.1103/PhysRevLett.78.4193 , Google ScholarCrossref
    O. V. Sosnovtseva, A. G. Balanov, T. E. Vadivasova, V. V. Astakhov, and E. Mosekilde, Phys. Rev. E 60, 6560 (1999). https://doi.org/10.1103/PhysRevE.60.6560 , , Google ScholarCrossref
  2. 2. L. Pecora and T. Carroll, Phys. Rev. Lett. 64, 821 (1990). https://doi.org/10.1103/PhysRevLett.64.821 , Google ScholarCrossref
  3. 3. M. Zhan, G. W. Wei, and C. H. Lai, Phys. Rev. E 65, 036202 (2002); https://doi.org/10.1103/PhysRevE.65.036202 , Google ScholarCrossref
    S. Taherion and Y. C. Lai, Phys. Rev. E 59, R6247 (1999); https://doi.org/10.1103/PhysRevE.59.R6247 , , Google ScholarCrossref
    P. K. Roy, S. Chakraborty, and S. K. Dana, Chaos 13(1), 342 (2003). https://doi.org/10.1063/1.1544734 , , Google ScholarScitation
  4. 4. J. N. Blakely, M. W. Pruitt, and N. J. Corron, Chaos 18, 013117 (2008); https://doi.org/10.1063/1.2840778 , Google ScholarScitation
    N. J. Corron, J. N. Blakely, and S. D. Pethel, Chaos 15, 023110 (2005); https://doi.org/10.1063/1.1898597 , , Google ScholarScitation
    N. J. Corron, J. N. Blakely, and S. D. Pethel, in Proceedings of the 8th Experimental Chaos Conference, (2004), Vol. 742, pp. 45–50. , Google Scholar
  5. 5. V. Senthilkumar and M. Lakshmanan, Phys. Rev. E 71, 016211 (2005); https://doi.org/10.1103/PhysRevE.71.016211 , Google ScholarCrossref
    E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, Phys. Lett. A 292, 320 (2002); https://doi.org/10.1016/S0375-9601(01)00824-6 , , Google ScholarCrossref
    S. Sivaprakasam, P. S. Spencer, P. Rees, and K. A. Shore, Opt. Lett. 27, 1250 (2002); https://doi.org/10.1364/OL.27.001250 , , Google ScholarCrossref
    D. Ghosh, I. Grosu, and S. K. Dana, Chaos 22, 033111 (2012). https://doi.org/10.1063/1.4731797 , , Google ScholarScitation
  6. 6. S. Boccaletti and D. L. Valladares, Phys. Rev. E 62, 7497 (2000). https://doi.org/10.1103/PhysRevE.62.7497 , Google ScholarCrossref
  7. 7. E. Bullmore and O. Sporns, Nat. Rev. Neurosci. 10, 186 (2009). https://doi.org/10.1038/nrn2575 , Google ScholarCrossref
  8. 8. W.-Q. Huang, X.-T. Zhuang, and S. Yao, Physica A 388, 2956 (2009). https://doi.org/10.1016/j.physa.2009.03.028 , Google ScholarCrossref
  9. 9. A. K. Engel, P. König, A. K. Kreiter, and W. Singer, Science 252, 1177 (1991); https://doi.org/10.1126/science.252.5009.1177 , Google ScholarCrossref
    P. R. Roelfsema, A. K. Engel, P. König, and W. Singer, Nature (London) 385, 157 (1997). https://doi.org/10.1038/385157a0 , , Google ScholarCrossref
  10. 10. J. Tiana-Alsina, J. H. Garcia-Lopez, M. C. Torrent, and J. Garcia-Ojalvo, Chaos 21, 043102 (2011). https://doi.org/10.1063/1.3644392 , Google ScholarScitation
  11. 11. I. Grosu, E. Padmanaban, P. K. Roy, and S. K. Dana, Phys. Rev. Lett. 100, 234102 (2008); https://doi.org/10.1103/PhysRevLett.100.234102 , Google ScholarCrossref
    I. Grosu, R. Banerjee, P. K. Roy, and S. K. Dana, Phys. Rev. E 80, 016212 (2009); https://doi.org/10.1103/PhysRevE.80.016212 , , Google ScholarCrossref
    P. K. Roy, C. Hens, I. Grosu, and S. K. Dana, Chaos 21, 013106 (2011); https://doi.org/10.1063/1.3539802 , , Google ScholarScitation
    E. A. Jackson and I. Grosu, Physica D 85, 1 (1995); https://doi.org/10.1016/0167-2789(95)00171-Y , , Google ScholarCrossref
    I. Grosu, Phys. Rev. E 56, 3709 (1997); https://doi.org/10.1103/PhysRevE.56.3709 , , Google ScholarCrossref
    I. Grosu, Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 3519 (2007). https://doi.org/10.1142/S0218127407019299 , , Google ScholarCrossref
  12. 12. J. L. Hindmarsh and R. M. Rose, Proc. R. Soc., London, Ser. B 221, 87 (1984). https://doi.org/10.1098/rspb.1984.0024 , Google ScholarCrossref
  13. 13. O. E. Rössler, Phys. Lett. A 57, 397 (1976). https://doi.org/10.1016/0375-9601(76)90101-8 , Google ScholarCrossref
  14. 14. J. C. Sprott, Phys. Rev. E 50, R647 (1994). https://doi.org/10.1103/PhysRevE.50.R647 , Google ScholarCrossref
  15. 15. R. C. Dorf and R. H. Bishop, Modern Control Systems (Prentice-Hall, 2001); Google Scholar
    A. Hurwitz, “ On the conditions under which an equation has only roots with negative real parts,” in Selected Papers on Mathematical Trends in Control Theory, edited by R. T. Ballman and R. Kalaba (Dover, New York, 1964). Google Scholar
  16. 16. S. K. Bhowmick, P. Pal, P. K. Roy, and S. K. Dana, Chaos 22, 023151 (2012). https://doi.org/10.1063/1.4731263 , Google ScholarScitation
  1. © 2013 AIP Publishing LLC.
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Proin imperdiet nibh sed ipsum molestie eu mattis justo malesuada. Curabitur id quam augue, ac eleifend justo. Integer eget metus sagittis velit semper auctor vel et nunc. Phasellus tempus felis at arcu fringilla at ndimentum libero placerat. Aenean ut imperdiet dolor. Nulla pretium mi vestibulum dui dictum sed ullamcorper tellus sodales. Duis non nibh id ipsum feugiat imperdiet id fermentum nunc. Maecenas id ultricies felis. Suspendisse lacinia rhoncus vestibulum. Vestibulum molestie vulputate convallis.Fusce et augue erat, nec mollis mi.