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Solitonlike and nonsoliton modes of interaction of taxis waves (illustrated with an example of bacterial population waves)

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Abstract

It was shown earlier that during collisions bacterial population waves may either penetrate one another or stop. In this communication, the mechanism of these two interaction modes is considered in detail. It is shown on the basis of theoretical and experimental results that this interaction is a graphic example confirming one of the characteristic properties of waves in cross-diffusion systems.

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References

  1. G. R. Ivanitsky, A. B. Medvinsky, and M. A. Tsyganov, Usp. Fiz. Nauk 161(4), 13 (1991).

    Google Scholar 

  2. G. R. Ivanitsky, A. B. Medvinsky, and M. A. Tsyganov, Usp. Fiz. Nauk 164(10), 1041 (1994).

    Google Scholar 

  3. J. Adler, Science 153, 708 (1966).

    Article  ADS  Google Scholar 

  4. J. Adler, Bacteriol. 92, 121 (1966).

    Google Scholar 

  5. E. O. Budrene, Biofizika 33, 373 (1988).

    Google Scholar 

  6. K. Agladze, E. Budrene, G. Ivanitsky, et al., Proc. Roy. Soc. Lond. B 253, 131 (1993).

    Article  ADS  Google Scholar 

  7. E. F. Keller and L. A. Segel, J. Theor. Biol. 30, 225 (1971).

    Article  Google Scholar 

  8. M. A. Tsyganov, I. B. Kresteva, A. B. Medvinsky, and G. R. Ivanitsky, Dokl. RAN 333(4), 532 (1993).

    Google Scholar 

  9. D. E. Koshland, Jr., Physiol. Rev. 59, 811 (1979).

    Google Scholar 

  10. A. B. Medvinsky, M. A. Tsyganov, I. B. Kresteva, et al., Physica D 64, 267 (1993).

    Article  MATH  ADS  Google Scholar 

  11. M. A. Tsyganov, J. Brindley, A. V. Holden, and V. N. Biktashev, Phys. Rev. Lett. 91(21), 218102 (2003).

    Google Scholar 

  12. M. A. Tsyganov, J. Brindley, A. V. Holden, and V. N. Biktashev, Physica D 197(1–2), 18 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. M. A. Tsyganov and V. N. Biktashev, Phys. Rev. E 70(3), 031901 (2004).

    Google Scholar 

  14. V. N. Biktashev, J. Brindley, A. V. Holden, and M. A. Tsyganov, Chaos 14(4), 988 (2004).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. J. E. Truscott and J. Brindley, Philos. Trans. R. Soc. A 374, 703 (1994).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, J. Phys. Chem. B 102, 4966 (1998).

    Article  Google Scholar 

  18. O. A. Mornev, O. V. Aslandi, R. R. Aliev, and L. M. Chailakhyan, Dokl. Ross. Akad. Nauk 347, 123 (1998).

    Google Scholar 

  19. O. V. Aslandi and O. A. Mornev, Biofizika 41(5), 953 (1996).

    Google Scholar 

  20. V. N. Biktashev and M. A. Tsyganov, Proc. Roy. Soc. Lond. A 461, 3711 (2005).

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Book  MATH  Google Scholar 

  22. A. J. Perumpanani, J. A. Sherratt, and J. Norbury, Nonlinearity 10, 1599 (1997).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. A. J. Perumpanani and H. M. Byrne, Eur. J. Cancer 35(8), 1274 (1999).

    Article  Google Scholar 

  24. J. A. Sherratt, J. Math. Biol. 43, 297 (2001).

    Article  MathSciNet  Google Scholar 

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Original Russian Text © M.A. Tsyganov, G.R. Ivanitsky, 2006, published in Biofizika, 2006, Vol. 51, No. 6, pp. 1008–1013.

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Tsyganov, M.A., Ivanitsky, G.R. Solitonlike and nonsoliton modes of interaction of taxis waves (illustrated with an example of bacterial population waves). BIOPHYSICS 51, 887–891 (2006). https://doi.org/10.1134/S0006350906060066

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  • DOI: https://doi.org/10.1134/S0006350906060066

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