- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Amplitude death through a Hopf bifurcation in coupled electrochemical oscillators: Experiments and simulations

Yumei Zhai, István Z. Kiss, and John L. Hudson*

  • Department of Chemical Engineering, 102 Engineers’ Way, University of Virginia, Charlottesville, Virginia 22904-4741, USA

  • *Electronic address: hudson@virginia.edu
PDF

Phys. Rev. E 69, 026208 – Published 27 February, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.026208

Abstract

Amplitude death was observed in experiments with two coupled periodic electrochemical oscillators without time delay. Simulation results confirmed that the observed amplitude death was obtained via a Hopf bifurcation. The two oscillators must have a minimum discrepancy and both be near their individual Hopf bifurcations for amplitude death to occur. Phase drift (coexisting with unstable asymmetric phase-locked solutions), amplitude death, and in-phase synchronization were observed in both the experiments and simulations as coupling strength was increased. In addition, the simulations showed that a stable asymmetric phase-locked solution exists between the phase drift and amplitude death regions.

View figure in article

References (33)

  1. Y. Kuramoto, Chemical Oscillations, Waves and Turbulence (Springer, Berlin, 1984).
  2. A.T. Winfree, The Geometry of Biological Time (Springer-Verlag, New York, 1980).
  3. G.B. Ermentrout and N. Kopell, SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 50, 125 (1990).
  4. R.A. Oliva and S.H. Strogatz, Int. J. Bifurcation Chaos Appl. Sci. Eng. 11, 2359 (2001).
  5. G. Ertl, Science 254, 1750 (1991).
  6. A.K. Ghosh, B. Chance, and E.K. Pye, Arch. Biochem. Biophys. 145, 319 (1971).
  7. A.T. Winfree, J. Theor. Biol. 16, 15 (1967).
  8. D.C. Michaels, E.P. Matyas, and J. Jalife, Circ. Res. 61, 704 (1987).
  9. H. Daido, Physica D 91, 24 (1996).
  10. S.H. Strogatz, Physica D 143, 1 (2000).
  11. A.S. Pikovksy, M.G. Rosenblum, and J. Kurths, Synchronization: A Universal Concept in Nonlinear Science (Univeristy Press, Cambridge, 2001).
  12. I.Z. Kiss, Y.M. Zhai, and J.L. Hudson, Science 296, 1676 (2002).
  13. K. Bar-Eli, Physica D 14, 242 (1985).
  14. M.F. Crowley and I.R. Epstein, J. Phys. Chem. 93, 2496 (1989).
  15. D.G. Aronson, G.B. Ermentrout, and N. Kopell, Physica D 41, 403 (1990).
  16. M. Dolnik and I.R. Epstein, Phys. Rev. E 54, 3361 (1996).
  17. A. Stefanski and T. Kapitaniak, Phys. Lett. A 210, 279 (1996).
  18. D.V.R. Reddy, A. Sen, and G.L. Johnston, Phys. Rev. Lett. 80, 5109 (1998).
  19. R. Herrero, M. Figueras, J. Rius, F. Pi, and G. Orriols, Phys. Rev. Lett. 84, 5312 (2000).
  20. D.V.R. Reddy, A. Sen, and G.L. Johnston, Phys. Rev. Lett. 85, 3381 (2000).
  21. L.L. Rubchinsky, M.M. Sushchik, and G.V. Osipov, Math. Comput. Simul. 58, 443 (2002).
  22. K. Kaneko, Phys. Rev. Lett. 63, 219 (1989).
  23. D.H. Zanette and A.S. Mikhailov, Phys. Rev. E 62, R7571 (2000).
  24. W. Wang, I.Z. Kiss, and J.L. Hudson, Chaos 10, 248 (2000).
  25. K. Bar-Eli, J. Phys. Chem. 88, 6174 (1984).
  26. K. Bar-Eli and S. Reuveni, J. Phys. Chem. 89, 1329 (1985).
  27. K. Bar-Eli, J. Phys. Chem. 88, 3616 (1984).
  28. M. Yoshimoto, Chem. Phys. Lett. 280, 539 (1997).
  29. G.B. Ermentrout, Physica D 41, 219 (1990).
  30. D.V.R. Reddy, A. Sen, and G.L. Johnston, Physica D 129, 15 (1999).
  31. I.Z. Kiss, W. Wang, and J.L. Hudson, J. Phys. Chem. B 103, 11 433 (1999).
  32. L. Rubchinsky and M. Sushchik, Phys. Rev. E 62, 6440 (2000).
  33. D. Haim, O. Lev, L.M. Pismen, and M. Sheintuch, J. Phys. Chem. 96, 2676 (1992).

Outline

Information

Phys. Rev. E 69, 026208– Published 27 February, 2004
  • Received 9 September 2003

© 2004 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation