Russian version English version
Volume 12   Issue 1   Year 2017
Sidorova A.E., Levashova N.T., Melnikova A.ΐ., Semina A.E.

The Model of Structurization of Urban Ecosystems as the Process of Self-Organization in Active Media

Mathematical Biology & Bioinformatics. 2017;12(1):186-197.

doi: 10.17537/2017.12.186.



  1. Helbich M., Leitner M. Postuburban spatial evolution of Vienna’s Urban Fringe: evidence from point process modeling. Urban Geography. 2010;31(8):1100-1117. doi: 10.2747/0272-3638.31.8.1100
  2. Yorgos Y. Papageorgiou. Population density in a central-place system. Journal of Regional Science. 2014;54(3):450-461.
  3. Vaz E., Arsanjani J.J. Predicting urban growth of the Greater Toronto Area – coupling a markov cellular automata with document meta-analysis. Journal of Environmental Informatics. 2015;25(2):71-80. doi: 10.3808/jei.201500299
  4. Frankhauser P. Fractal geometry of urban patterns and their morphogenesis. Discrete Dynamics in Nature and Society. 1998;2(2):127-145. doi: 10.1155/S1026022698000107
  5. Sidorova A.E., Levashova N.T., Melnikova A.A., Yakovenko L.V. A model of a human dominated urban ecosystem as an active medium. Biophysics. 2015;60(3):466-473. doi: 10.1134/S0006350915030185
  6. Sidorova A.E., Mukhartova Yu.V., Yakovenko L.V. An urban ecosystem as a superposition of interrelated active media. Moscow University Physics Bulletin. 2014;69(5):392-400. doi: 10.3103/S0027134914050087
  7. Sidorova A.E., Levashova N.T., Melnikova A.A., Deryugina N.N., Semina A.E. Autowave self-organization in heterogeneous natural-anthropogenic ecosystems. Moscow University Physics Bulletin. 2016;71(6):562-568. doi: 10.3103/S0027134916050167
  8. Levashova N., Melnikova A., Semina A., Sidorova A. Autowave mechanisms of structure formation in urban ecosystems as the process of self-organization in active media. Communication on Applied Mathematics and Computation. 2017;31(1):32-42.
  9. Murray J.D. Mathematical Biology II: Spatial Models and Biomedical Applications. Berlin Heidelberg: Springer-Verlag; 2003. 811 p.
  10. El'kin Yu.E. Autowave processes. Mathematical Biology and Bioinformatics. 2006;1(1):27-40 (in Russ.). doi: 10.17537/2006.1.27
  11. Vasiliev V.A., Romanovsky Yu.M., Yakhno V.G. Autowave Processes. Moscow: Nauka; 1987. 240 p. (in Russ.). doi: 10.1007/978-94-009-3751-2
  12. Romanovsky Yu.M., Stepanova N.V., Chernavsky D.S. Mathematical Biophysics. Moscow: Nauka; 1984. 304 p. (in Russ.).
  13. Tverdislov V.A., Malyshko E.V., Ilchenko S.A. From autowave mechanisms of self-assembly to molecular machines. Bulletin of the Russian Academy of Sciences: Physics. 2015;79(12):1516-1520. doi: 10.3103/S1062873815120230
  14. Savenko V.S. Geochemical aspects of sustainable development. M.: GEOS; 2003. 180 p.
  15. FitzHugh R.A. Impulses and physiological states in theoretical model of nerve membrane. Biophys. J. 1961:445-466. doi: 10.1016/S0006-3495(61)86902-6
  16. Kalitkin N.N., Koryakin P.V. Chislennye metody. V 2 kn. Kn. 2. Metody matematicheskoi fiziki (Numerical methods. In 2 books. Book 2. Methods of Mathematical Physics). Moscow: Akademiya Publ.; 2013. 303 p. (in Russ.).
  17. Samarsky A.A., Gulin A.V. Chislennye metody matematicheskoi fiziki (Numerical Methods of Mathematical Physics). Moscow; 2003. 316 p. (in Russ.).
  18. Butuzov V.F., Levashova N.T., Mel'nikova A.A. Steplike contrast structure in a singularly perturbed system of equations with different powers of small parameter. Computational Mathematics and Mathematical Physics. 2012;52(11):1526-1546. doi: 10.1134/S096554251211005X
  19. Butuzov V.F., Levashova N.T., Mel'nikova A.A. A steplike contrast structure in a singularly perturbed system of elliptic equations. Computational Mathematics and Mathematical Physics. 2013;53(9):1239-1259. doi: 10.1134/S0965542513090054
  20. Retromap. (accessed 20 April 2017).
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2017.12.186
published in Russian

Abstract (rus.)
Abstract (eng.)
Full text (rus., pdf)


  Copyright IMPB RAS © 2005-2024