ABSTRACT
We experimentally demonstrate that a processing delay, a finite response time, in the coupling can revoke the stability of the stable steady states, thereby facilitating the revival of oscillations in the same parameter space where the coupled oscillators suffered the quenching of oscillation. This phenomenon of reviving of oscillations is demonstrated using two different prototype electronic circuits. Further, the analytical critical curves corroborate that the spread of the parameter space with stable steady state is diminished continuously by increasing the processing delay. Finally, the death state is completely wiped off above a threshold value by switching the stability of the stable steady state to retrieve sustained oscillations in the same parameter space. The underlying dynamical mechanism responsible for the decrease in the spread of the stable steady states and the eventual reviving of oscillation as a function of the processing delay is explained using analytical results.
D.V.S. was supported by the SERB-DST Fast Track scheme for young scientist under Grant No. ST/FTP/PS-119/2013. K.S. acknowledges the DST, India, and the Bharathidasan University for financial support under the DST-PURSE programme. The work of V.K.C. was supported by the INSA young scientist project. W.Z. acknowledges the financial support from the National Natural Science Foundation of China under Grant No. 11202082. K.T. acknowledges the DST, India, for financial support. S.K.D. was supported by the CSIR Emeritus scientist scheme.
REFERENCES
- 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. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence ( Springer, Berlin, 1984). Google ScholarCrossref
- 4. W. L. Koukkari and R. B. Sothern, Introducing Biological Rhythms ( Springer, Berlin, 2006). Google Scholar
- 5. M. Lakshmanan and D. V. Senthilkumar, Dynamics of Nonlinear Time-Delay Systems ( Springer, Berlin, 2010). Google Scholar
- 6. G. Saxena, A. Prasad, and R. Ramaswamy, Phys. Rep. 521, 205 (2012). https://doi.org/10.1016/j.physrep.2012.09.003, Google ScholarCrossref
- 7. A. Koseska, E. Volkov, and J. Kurths, Phys. Rep. 531, 173–199 (2013). https://doi.org/10.1016/j.physrep.2013.06.001, Google ScholarCrossref
- 8.
J. W. S. Rayleigh, The Theory of Sound, Vol. 2 (
Dover Publications, 1945); Google Scholar
M. Abel, K. Ahnert, and S. Bergweiler, Phys. Rev. Lett. 103, 114301 (2009). https://doi.org/10.1103/PhysRevLett.103.114301, Google ScholarCrossref - 9. K. Bar-Eli, Physica D 14, 242 (1985). https://doi.org/10.1016/0167-2789(85)90182-4, Google ScholarCrossref
- 10. G. B. Ermentrout and N. Kopel, SIAM J. Appl. Math. 50, 125–146 (1990). https://doi.org/10.1137/0150009, Google ScholarCrossref
- 11.
B. F. Kuntsevich and
A. N. Pisarchik, Phys. Rev. E 64, 046221 (2001); https://doi.org/10.1103/PhysRevE.64.046221, Google ScholarCrossref
A. Prasad, Y. C. Lai, A. Gavrielides, and V. Kovanis, Phys. Lett. A 318, 71 (2003); https://doi.org/10.1016/j.physleta.2003.08.072, , Google ScholarCrossref
M. Y. Kim, R. Roy, J. L. Aron, T. W. Carr, and I. B. Schwartz, Phys. Rev. Lett. 84, 088101 (2005). https://doi.org/10.1103/PhysRevLett.94.088101, , Google ScholarCrossref - 12. D. V. R. Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. 85, 3381–3384 (2000). https://doi.org/10.1103/PhysRevLett.85.3381, Google ScholarCrossref
- 13. I. Ozden, S. Venkataramani, M. A. Long, B. W. Connors, and A. V. Nurmikko, Phys. Rev. Lett. 93, 158102 (2004). https://doi.org/10.1103/PhysRevLett.93.158102, Google ScholarCrossref
- 14. A. Koseska, E. Volkov, and J. Kurths, Phys. Rev. Lett. 111, 024103 (2013). https://doi.org/10.1103/PhysRevLett.111.024103, Google ScholarCrossref
- 15. C. R. Hens, O. I. Olusola, P. Pal, and S. K. Dana, Phys. Rev. E 88, 034902 (2013). https://doi.org/10.1103/PhysRevE.88.034902, Google ScholarCrossref
- 16. C. R. Hens, P. Pal, S. K. Bhowmick, P. K. Roy, A. Sen, and S. K. Dana, Phys. Rev. E 89, 032901 (2014). https://doi.org/10.1103/PhysRevE.89.032901, Google ScholarCrossref
- 17.
W. Zou,
D. V. Senthilkumar,
A. Koseska, and
J. Kurths, Phys. Rev. E 88, 050901(R) (2013); https://doi.org/10.1103/PhysRevE.88.050901, Google ScholarCrossref
W. Zou, D. V. Senthilkumar, J. Duan, and J. Kurths, Phys. Rev. E 90, 032906 (2014). https://doi.org/10.1103/PhysRevE.90.032906, , Google ScholarCrossref - 18.
T. Banerjee and
D. Ghosh, Phys. Rev. E 89, 052912 (2014); https://doi.org/10.1103/PhysRevE.89.052912, Google ScholarCrossref
T. Banerjee and D. Ghosh, Phys. Rev. E 89, 062902 (2014); , Google ScholarCrossref
D. Ghosh, T. Banerjee, and J. Kurths, Phys. Rev. E 92, 052908 (2015). https://doi.org/10.1103/PhysRevE.92.052908, , Google ScholarCrossref - 19. M.-D. Wei and J.-C. Lun, Appl. Phys. Lett. 91, 061121 (2007). https://doi.org/10.1063/1.2769757, Google ScholarScitation, ISI
- 20. D. Kondor and G. Vattay, PLoS One 8, e57653 (2013). https://doi.org/10.1371/journal.pone.0057653, Google ScholarCrossref
- 21.
E. Ullner,
A. Zaikin,
E. I. Volkov, and
J. García-Ojalvo, Phys. Rev. Lett. 99, 148103 (2007); https://doi.org/10.1103/PhysRevLett.99.148103, Google ScholarCrossref
A. Koseska, E. Ullner, E. Volkov, J. Kurths, and J. García-Ojalvo, J. Theor. Biol. 263, 189 (2010). https://doi.org/10.1016/j.jtbi.2009.11.007, , Google ScholarCrossref - 22.
K. Konishi, Phys. Lett. A 341, 401–409 (2005); https://doi.org/10.1016/j.physleta.2005.04.094, Google ScholarCrossref
K. Morino, G. Tanaka, and K. Aihara, Phys. Rev. E 88, 032909 (2013). https://doi.org/10.1103/PhysRevE.88.032909, , Google ScholarCrossref - 23. A. Majdandzic, B. Podobnik, S. V. Buldyrev, D. Y. Kenett, S. Havlin, and H. E. Stanely et al., Nat. Phys. 10, 34–38 (2014). https://doi.org/10.1038/nphys2819, Google ScholarCrossref
- 24. W. Zou, C. Yao, and M. Zhan, Phys. Rev. E 82, 056203 (2010). https://doi.org/10.1103/PhysRevE.82.056203, Google ScholarCrossref
- 25. W. Zou, D. V. Senthilkumar, and J. Kurths, Phys. Rev. Lett. 111, 014101 (2013). https://doi.org/10.1103/PhysRevLett.111.014101, Google ScholarCrossref
- 26. D. V. Ramana Reddy, A. Sen, and G. L. Johnston, Phys. Rev. Lett. 80, 5109 (1998). https://doi.org/10.1103/PhysRevLett.80.5109, Google ScholarCrossref
- 27. W. Zou, D. V. Senthilkumar, R. Nagao, I. Z. Kiss, Y. Tang, A. Koseska, J. Duan, and J. Kurths, Nat. Commun. 6, 7709 (2015). https://doi.org/10.1038/ncomms8709, Google ScholarCrossref
- 28. A. Szucs, P. Varona, A. R. Volkovskii, H. D. I. Abarbanel, M. I. Rabinovich, and A. I. Selverston, Neuroreport 11(3), 563 (2000). https://doi.org/10.1097/00001756-200002280-00027, Google ScholarCrossref
- 29.bc = (−4ε3−2ε4 + 40ε5 + 20ε6 − 136ε7 − 48ε8 + 219ε9 + 25ε10 − 193ε11 + 29ε12 + 118ε13 − 22ε14 − 63ε15 − 5ε16 + 18ε17 + 6ε18)(−1 − ε + 2ε2 + 21ε4 + 43ε5−119ε6−183ε7+318ε8+328ε9−526ε10−300ε11 + 514ε12 + 162ε13 −258ε14−70ε15 + 54ε16 + 18ε17)−1.
- 30. See supplementary material at http://dx.doi.org/10.1063/1.4947081 for analog circuits, circuit equation, normalized equation, and analytical procedures. Google Scholar
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