Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Contemporary problems and examples of alternative chaotic regimes in the simulation of environmental processes


A.U. Perevarukha − Ph.D. (Eng.), Senior Research Scientist, Laboratory of Applied Informatics, St. Petersburg Institute of Informatics and Automation of the Russian Academy of Science (SPIIRAS). E-mail:

Article goes on a series of papers about the problems of the application of nonlinear effects in the iterative model for describing the environmental processes that are accompanied by structural changes. Determination of the conditions of transformation between the states is one of the tasks of strategic planning in environmental management. In the practice of modeling ecosystem dynamics we write deterministic equations, but they do not guarantee freedom from the statistical confusion. Feature of the models, which are able to describe the nonlinear relationship between the interacting factors, is the emergence of irregular regime, almost random mo-tion path with fixed parameters. The reasons of explicit inconsistencies qualitative nature and absence of predictive capabilities of models, consisting of the key problem with availability of the essential biological interpretation several nonlinear effects in the dynam-ics of one-dimensional maps are shown. For understanding principles of the development of new hybrid models it is useful to consid-er aspects of finding uncertainty in the behavior of different types of computational models. Lorenz found that there is a fundamental inability to make long-term forecasts based on the selected private investigator computational structure due to the properties of the exponential divergence of trajectories with initial points in one small ε-neighborhood. Chaotic movement trajectory is determined by the presence of «strange» geometrical shape of the attractor. Chaos on a countable set is impossible. The calculation of applied eco-logical problems with the introduction of discreteness in units eliminates the strange attractor. For the purposes of ecology presence of bifurcation is an important problem of interpretation of the simulation results. Bifurcation parameter of the model reflects the thoughts of developer effect of a particular factor. Qualitative changes in the results of the calculations should be explained from the standpoint of the subject area and to formulate practical conclusions about the consequences of changes in the action factor. After formalizing the ecological and physiological characteristics of the reproductive cycle of the insect we obtained a specialized model of the explosive growth in the number of forest pests. Qualitative changes in the dynamics we were able to obtain without explicitly de-scribing site-specific trophy interactions. We used a special functionality, resulting in a reduction of the fixed point. Of all the possible iterations for nonlinear effects in our approach uses only having a meaningful interpretation for population biology. Chaotic traffic is associated not with a strange attractor, and the presence of the set are not attracted to the attractor points.


  1. Gunderson L.H., Allen C.R., Holling C.S.Foundations of Ecological Resilience. Washington: Island Press. 2009. 496 p.
  2. Touhey P. Yet another definition of chaos // Amer. Math. Monthly. 1997. V. 104.5. P. 411–414.
  3. Lorenz E.N. Deterministic Nonperiodic Flow // Journal of the Atmospheric Sciences. 1963. V. 20.2. P. 130–141.
  4. Pesin JA.B.KHarakteristicheskie pokazateli Ljapunova i gladkaja ehrgodicheskaja teorija//Uspekhi matematicheskikh nauk. 1977. T. 32. № 4. S. 55–112
  5. Andronov A.A., Vitt A.A., KHajjkin S.EH.Teorija kolebanijj.M. 1959. 916s.
  6. Landau L.D., Lifshic E.M.Teoreticheskaja fizika. Gidrodinamika. Izd. 3-e, ispr. 1986.736 s. 
  7. Kolesov A.JU., Rozov N.KH., Sadovnichijj V.A. Matematicheskie aspekty teorii razvitija turbulentnosti po Landau//Uspekhimatematicheskikh nauk. 2008. T. 63. Vyp. 2. S. 21–84.
  8. Ruelle D., Takens F. On the nature of turbulence // Communication in Mathematical Physics. 1971. V. 20. P. 167–192.
  9. Perevarjukha A.JU.KHaoticheskie rezhimy v modeljakh teorii formirovanija popolnenija populjacijj//Nelinejjnyjj mir. 2009. T.7. № 12. S. 925−932.
  10. Feigenbaum M.J. Universal behavior in nonlinear systems // Physica D. 1983. V. 7.1–3. P. 16–39.
  11. Perevarjukha A.JU.Interpretacija povedenija modelejj dinamiki bioresursov i momentalnaja khaotizacija v novojj modeli//Nelinejjnyjj mir. 2012. T. 10. № 4. S. 255−262.
  12. Singer D. Stable orbits and bifurcations of the maps on the interval // SIAM journal of applied math. 1978. V. 35. P. 260–268.
  13. Veshhev P.V., Guteneva G.I.EHffektivnost estestvennogo vosproizvodstva osetrovykh v nizovjakh Volgi v sovremennykh uslovijakh // EHkologija. 2012. № 2. S. 123–128.
  14. Grebogi C., Ott E., Yorke J. Chaos, strange attractors and fractal basin boundaries in nonlinear dynamics // Science. 1987. V. 238.№ 4827. P. 632–638.
  15. Dettlaff T.A., Ginsburg A.S., Schmallhausen O.I. Sturgeon Fishes: Developmental Biology and Aquaculture. Springer-Verlag. 1993.234 p.
  16. Perevarjukha T.JU., Geraskin P.P., Perevarjukha JU.N., Melnik I.V. EHkologicheskie rasy sevrjugi(Acipenserstellatus)podannym immunokhimicheskogo analiza antigennogo sostava ikh syvorotochnykh belkov // Estestvennye nauki. 2010. № 3. S. 134−141.
  17. Cornulier T., Yoccoz N. G., Bretagnolle V., et al. Europe-Wide Dampening of Population Cycles in Keystone Herbivores // Science.2013. V. 340. P. 63–66. 


© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio