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Rotating bound states of dissipative solitons in systems of reaction-diffusion type

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Abstract

We report on the formation of stable rotating bound states consisting of self-organized well localized solitary structures with particle-like behaviour in systems of reaction-diffusion type. These dissipative solitons are detected in an experimental planar d.c. gas-discharge system with a high ohmic barrier, as well as in numerical solutions of related three-component reaction-diffusion equations where the formation of rotating bound states is investigated in the context of a particle ansatz.

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References

  1. M. Bode, H.-G. Purwins, Physica D 86, 53 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. C.I. Christov, M.G. Velarde, Physica D 86, 323 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)

    Google Scholar 

  4. Q. Ouyang, V. Castets, J. Boissonade, J.C. Roux, P. De Kepper, H.L. Swinney, J. Chem. Phys. 95, 351 (1991)

    Article  ADS  Google Scholar 

  5. H.H. Rotermund, S. Jakubith, A. von Oertzen, G. Ertl, Phys. Rev. Lett. 66, 3083 (1991)

    Article  ADS  Google Scholar 

  6. K.-Jin Lee, W.D. McCormick, J.E. Pearson, H.L. Swinney, Nature 369, 215 (1994)

    Article  ADS  Google Scholar 

  7. F.T. Arecchi, S. Boccaletti, P. Ramazza, Phys. Rep. 1-2, 1 (1999)

  8. T. Ackemann, W. Lange, Appl. Phys. B 72, 21 (2001)

    Article  ADS  Google Scholar 

  9. V.V. Bel’kov, J. Hirschinger, V. Novák, F.J. Niedernostheide, S.D. Ganichev, W. Prettl, Nature 397, 398 (1999)

    Article  ADS  Google Scholar 

  10. K. Aoki, Nonlinear Dynamics and Chaos in Semiconductors (Institute of Physics Publishing, Bristol and Philadelphia, 2001)

  11. E. Schöll, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors, Vol. 10 of Cambridge Nonlinear Science Series (Cambridge University Press, Cambridge, 2001)

  12. Y.A. Astrov, H.-G. Purwins, Phys. Lett. A 283, 349 (2001)

    Article  ADS  Google Scholar 

  13. I. Brauer, Experimentelle und numerische Untersuchungen zur Strukturbildung in dielektrischen Barriereentladungen, Dissertation, Institut für Angewandte Physik, Westfälische Wilhelms-Universität Münster, 2000

  14. A.W. Liehr, H.U. Bödeker, M.C. Röttger, T. Frank, R. Friedrich, H.-G. Purwins, New J. Phys. 5, 1 (2003); URL: http://stacks.iop.org/1367-2630/5/89

    Article  Google Scholar 

  15. J.D. Murray, Mathematical Biology (Springer, Berlin, 1993)

  16. M. Bode, A.W. Liehr, C.P. Schenk, H.-G. Purwins, Physica D 161, 45 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. B.S. Kerner, V.V. Osipov, Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, volume 61 of Fundamental Theories of Physics (Kluwer Academic Publishers, Dordrecht, 1994)

  18. M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993)

    Article  ADS  Google Scholar 

  19. Yu.A. Astrov, Yu.A. Logvin, Phys. Rev. Lett. 79, 2983 (1997)

    Article  ADS  Google Scholar 

  20. A.G. Vladimirov, J.M. McSloy, D.V. Skryabin, W.J. Firth, Phys. Rev. E 65, 1 (2002)

    Google Scholar 

  21. T. Ohta, J. Kiyose, M. Mimura, J. Phys. Soc. Jpn 66, 1551 (1997)

    Article  ADS  MATH  Google Scholar 

  22. C.B. Muratov, V.V. Osipov, Eur. Phys. J. B 22, 213 (2001)

    Article  ADS  Google Scholar 

  23. A.W. Liehr, A.S. Moskalenko, M.C. Röttger, J. Berkemeier, H.-G. Purwins, Replication of dissipative solitons by many-particle interaction, in High Performance Computing in Science and Engineering ‘02. Transactions of the High Performance Computing Center Stuttgart (HLRS) 2002, edited by E. Krause, W. Jäger, p. 48-61 (Springer, 2003)

  24. Y. Nishiura, T. Teramoto, Kei-Ichi Ueda, Phys. Rev. E 67, 056210 (2003)

    Article  ADS  Google Scholar 

  25. Y. Nishiura, T. Teramoto, Kei-Ichi Ueda, Chaos 13, 962 (2003)

    Article  ADS  Google Scholar 

  26. H. Bödeker, M.C. Röttger, A.W. Liehr, T. Frank, R. Friedrich, H.-G. Purwins, Phys. Rev. E 67, 056220 (2003)

    Article  ADS  Google Scholar 

  27. E. Ammelt, Yu.A. Astrov, H.-G. Purwins, Phys. Rev. E 58, 7109 (1998)

    Article  ADS  Google Scholar 

  28. Yu.A. Astrov, L.M. Portsel, S.P. Teperick, H. Willebrand, H.-G. Purwins, J. Appl. Phys. 74, 2159 (1993)

    Article  ADS  Google Scholar 

  29. H. Bödeker, A.W. Liehr, M.C. Röttger, T.D. Frank, R. Friedrich, H.-G. Purwins, Measuring the interaction law of dissipative solitons (in preparation)

  30. V. Steinberg, G. Ahlers, D.S. Cannell, Physica Scripta 32, 534 (1985)

    Article  ADS  Google Scholar 

  31. J.P. Gollub, C.W. Meyer, Physica D 6, 337 (1983)

    Article  ADS  Google Scholar 

  32. C.A. Jones, M.R.E. Proctor, Phys. Lett. A 121, 224 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  33. M. Rabaud, Y. Couder, S. Michalland, Eur. J. Mech. B 10, 253 (1991)

    Google Scholar 

  34. L. Pan, J.R. de Bruyn, Phys. Rev. E 49, 483 (1994)

    Article  ADS  Google Scholar 

  35. G.H. Gunaratne, M. El-Hamdi, M. Gorman, Mod. Phys. Lett. B 10, 1379 (1996)

    Article  ADS  Google Scholar 

  36. H.-G. Purwins, C. Radehaus, J. Berkemeier, Zeitschrift für Naturforschung a 43, 17 (1988)

    Google Scholar 

  37. A.M. Turing, Phil. Trans. Roy. Soc. B 237, 37 (1952)

    Article  ADS  Google Scholar 

  38. A.W. Liehr, M. Bode, H.-G. Purwins, The generation of dissipative quasi-particles near Turing’s bifurcation in three-dimensional reaction-diffusion-systems, in High Performance Computing in Science and Engineering 2000. Transactions of the High Performance Computing Center, Stuttgart (HLRS) 2000, edited by E. Krause, W. Jäger, p. 425-439 (Springer, 2001)

  39. T. Ohta, M. Mimura, R. Kobayashi, Physica D 34, 115 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. C.B. Muratov, V.V. Osipov, J. Phys. A 33, 8893 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  41. C.P. Schenk, P. Schütz, M. Bode, H.-G. Purwins, Phys. Rev. E 57, 6480 (1998)

    Article  ADS  Google Scholar 

  42. K. Krischer, A. Mikhailov, Phys. Rev. Lett. 73, 3165 (1994)

    Article  ADS  Google Scholar 

  43. T. Ohta, Physica D 151, 61 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. C.P. Schenk, M. Or-Guil, M. Bode, H.-G. Purwins, Phys. Rev. Lett. 78, 3781 (1997)

    Article  ADS  Google Scholar 

  45. L. Schimansky-Geier, Ch. Zülicke, E. Schöll, Zeitschrift für Physik B 84, 433 (1991)

    Article  ADS  Google Scholar 

  46. L.M. Pismen, Phys. Rev. Lett. 86, 548 (2001)

    Article  ADS  Google Scholar 

  47. E.L. Gurevich, A.W. Liehr, Sh. Amiranashvili, H.-G. Purwins, Role of surface charges in dc gas-discharge systems with high-ohmic electrodes (to be published in Phys. Rev. E 69)

  48. M. Or-Guil, M. Bode, C.P. Schenk, H.-G. Purwins, Phys. Rev. E 57, 6432 (1998)

    Article  ADS  Google Scholar 

  49. P. Coullet, J. Lega, B. Houchmanzadeh, J. Lajzerowicz, Breaking chirality in nonequilibrium systems, Phys. Rev. Lett. 65, 1352 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  50. A. Hagberg, E. Meron, Nonlinearity 7, 805 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. A.S. Moskalenko, A.W. Liehr, H.-G. Purwins, Europhys. Lett. 63, 361 (2003)

    Article  ADS  Google Scholar 

  52. A.W. Liehr, A.S. Moskalenko, H.-G. Purwins, Transition from stationary to rotating bound states of dissipative solitons, in High Performance Computing in Science and Engineering ‘03. Transactions of the High Performance Computing Center Stuttgart (HLRS) 2003, edited by E. Krause, W. Jäger, M. Resch (Springer, 2004), pp. 225-234

  53. A.W. Liehr, Dissipative Solitonen in Reaktions-Diffusions-Systemen, thesis, Institut für Angewandte Physik, Westfälische Wilhelms-Universität Münster, 2003

  54. M. Bode, A.W. Liehr, C.P. Schenk, H.-G. Purwins, Erratum to Interaction of dissipative solitons: Particle-like behaviour of localized structures in a three-component reaction-diffusion system [Physica D 161, 45 (2002)], Physica D 165, 127 (2002)

    MathSciNet  MATH  Google Scholar 

  55. I.S. Aranson, L.M. Pismen, Phys. Rev. Lett. 84, 634 (2000)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Physik, Corrensstr. 2/4, 48149, Münster, Germany

    A. W. Liehr, A. S. Moskalenko, Yu. A. Astrov, M. Bode & H.-G. Purwins

  2. A.F. Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021, St. Petersburg, Russia

    Yu. A. Astrov

  3. Fraunhofer-Institut für Autonome Intelligente Systeme AIS, Schloss Birlinghoven, 53754, Sankt Augustin, Germany

    M. Bode

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  1. A. W. Liehr
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  2. A. S. Moskalenko
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  3. Yu. A. Astrov
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  4. M. Bode
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  5. H.-G. Purwins
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Correspondence to A. W. Liehr.

Additional information

Received: 15 July 2003, Published online: 15 March 2004

PACS:

89.75.Fb Structures and organization in complex systems - 82.40.Ck Pattern formation in reactions with diffusion, flow and heat transfer - 52.80.Tn Other gas discharges

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Liehr, A.W., Moskalenko, A.S., Astrov, Y.A. et al. Rotating bound states of dissipative solitons in systems of reaction-diffusion type. Eur. Phys. J. B 37, 199–204 (2004). https://doi.org/10.1140/epjb/e2004-00047-7

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