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.
Similar content being viewed by others
References
G. R. Ivanitsky, A. B. Medvinsky, and M. A. Tsyganov, Usp. Fiz. Nauk 161(4), 13 (1991).
G. R. Ivanitsky, A. B. Medvinsky, and M. A. Tsyganov, Usp. Fiz. Nauk 164(10), 1041 (1994).
J. Adler, Science 153, 708 (1966).
J. Adler, Bacteriol. 92, 121 (1966).
E. O. Budrene, Biofizika 33, 373 (1988).
K. Agladze, E. Budrene, G. Ivanitsky, et al., Proc. Roy. Soc. Lond. B 253, 131 (1993).
E. F. Keller and L. A. Segel, J. Theor. Biol. 30, 225 (1971).
M. A. Tsyganov, I. B. Kresteva, A. B. Medvinsky, and G. R. Ivanitsky, Dokl. RAN 333(4), 532 (1993).
D. E. Koshland, Jr., Physiol. Rev. 59, 811 (1979).
A. B. Medvinsky, M. A. Tsyganov, I. B. Kresteva, et al., Physica D 64, 267 (1993).
M. A. Tsyganov, J. Brindley, A. V. Holden, and V. N. Biktashev, Phys. Rev. Lett. 91(21), 218102 (2003).
M. A. Tsyganov, J. Brindley, A. V. Holden, and V. N. Biktashev, Physica D 197(1–2), 18 (2004).
M. A. Tsyganov and V. N. Biktashev, Phys. Rev. E 70(3), 031901 (2004).
V. N. Biktashev, J. Brindley, A. V. Holden, and M. A. Tsyganov, Chaos 14(4), 988 (2004).
J. E. Truscott and J. Brindley, Philos. Trans. R. Soc. A 374, 703 (1994).
H. H. Rotermund, S. Jakubith. A. von Oertzen, and G. Ertl, Phys. Rev. Lett. 66, 3083 (1991).
A. von Oertzen, A. S. Mikhailov, H. H. Rotermund, and G. Ertl, J. Phys. Chem. B 102, 4966 (1998).
O. A. Mornev, O. V. Aslandi, R. R. Aliev, and L. M. Chailakhyan, Dokl. Ross. Akad. Nauk 347, 123 (1998).
O. V. Aslandi and O. A. Mornev, Biofizika 41(5), 953 (1996).
V. N. Biktashev and M. A. Tsyganov, Proc. Roy. Soc. Lond. A 461, 3711 (2005).
J. D. Murray, Mathematical Biology (Springer, Berlin, 1993).
A. J. Perumpanani, J. A. Sherratt, and J. Norbury, Nonlinearity 10, 1599 (1997).
A. J. Perumpanani and H. M. Byrne, Eur. J. Cancer 35(8), 1274 (1999).
J. A. Sherratt, J. Math. Biol. 43, 297 (2001).
Author information
Authors and Affiliations
Additional information
Original Russian Text © M.A. Tsyganov, G.R. Ivanitsky, 2006, published in Biofizika, 2006, Vol. 51, No. 6, pp. 1008–1013.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0006350906060066