ABSTRACT
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.
ACKNOWLEDGMENTS
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.
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. L. Pecora and T. Carroll, Phys. Rev. Lett. 64, 821 (1990). https://doi.org/10.1103/PhysRevLett.64.821 , Google ScholarCrossref
- 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.
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.
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. S. Boccaletti and D. L. Valladares, Phys. Rev. E 62, 7497 (2000). https://doi.org/10.1103/PhysRevE.62.7497 , Google ScholarCrossref
- 7. E. Bullmore and O. Sporns, Nat. Rev. Neurosci. 10, 186 (2009). https://doi.org/10.1038/nrn2575 , Google ScholarCrossref
- 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.
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. 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.
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. 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. O. E. Rössler, Phys. Lett. A 57, 397 (1976). https://doi.org/10.1016/0375-9601(76)90101-8 , Google ScholarCrossref
- 14. J. C. Sprott, Phys. Rev. E 50, R647 (1994). https://doi.org/10.1103/PhysRevE.50.R647 , Google ScholarCrossref
- 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. 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
Please Note: The number of views represents the full text views from December 2016 to date. Article views prior to December 2016 are not included.

