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Analytical modeling and stability analysis of nonlinear broadband migration flows

Keywords:

I.N. Sinitsyn – Dr.Sc. (Eng.), Professor, Chief Research Scientist, FRС «Computer Science and Control» of RAS (Moscow)
E-mail: sinitsin@dol.ru
O.V. Druzhinina – Dr.Sc. (Phys.-Math.), Professor, Chief Research Scientist, FRС «Computer Science and Control» of RAS (Moscow)
E-mail: ovdruzh@mail.ru
O.N. Masina – Dr.Sc. (Phys.-Math.), Head of the Department «Mathematical Modeling and Computer Technologies», Bunin Yelets State University (Yelets)
E-mail: olga121@inbox.ru


Methodological support of analytical modeling of nonstationary processes in stochastic migratory-population differential systems is developed and the stability analysis of regular and irregular modes is carried out for the first two probabilistic moments. The problems of analysis and synthesis of multidimensional nonlinear dynamic models that describe migration flows are considered taking into account the effect of broadband parametric and additive noise. Analytical modeling of multidimensional migration flows under stochastic perturbations is based on the methods of normal approximation and statistical linearization. The stability of stationary states is investigated and the interpretation of the effects obtained for stochastic models is presented. For model examples, the properties of migratory-population systems are compared in deterministic and stochastic cases and the effects due to stochastic broadband per-turbations are revealed. The conducted researches have shown rather high efficiency of application of methods of analytical modeling to the description and the analysis of nonlinear broadband migratory flows.

References:
  1. Vol'terra V. Matematicheskaya teoriya bor'by za sushchestvovanie. M.: Nauka. 1976. 286 s. 
  2. Svirezhev YU.M. Nelinejnye volny, dissipativnye struktury i katastrofy v ehkologii. M.: Nauka. 1987. 368 s.
  3. McKane A., Newman T. Stochastic models in population biology and their deterministic analogs// Phys Rev E. 2004; 70(4):041902. https://doi.org/10.1103/PhysRevE.70.041902.
  4. Ovaskainen O., Meerson B. Stochastic models of population extinction// Trends Ecol Evol. 2010; 25(11):643–652. https://doi.org/10.1016/j.tree.2010.07.009 PMID: 20810188. 
  5. Tkachenko N., Weissmann J.D., Petersen W.P., Lake G., Zollikofer C.P.E., Callegari S. Individual-based modelling of population growth and diffusion in discrete time// PLoS ONE. 2017. 2(4): e0176101. https://doi.org/10.1371/journal.pone.0176101.
  6. Druzhinina O.V., Masina O.N. Metody issledovaniya ustojchivosti i upravlyaemosti nechetkih i stohasticheskih dinamicheskih sistem. M.: VC RAN. 2009. 178 s.
  7. Tuckwell H.C. A study of some diffusion models of population growth // Theoretical population bio-logy. 1974. V. 5. P. 345–357. 
  8. Zhang Xin-an, Chen Lansun. The linear and nonlinear diffusion of the competitive Lotka–Volterra model // Nonlinear Analysis. 2007. V. 66. P. 2767–2776. 
  9. Freedman H.I., Waltman P. Mathematical models of population interaction with dispersal I: Stability of habitats with and without a predator // SIAM J. Appl. Math. 1977. V. 32. P. 631–648. 
  10. Freedman H.I., Rai B., Waltman P. Mathematical models of population interaction with dispersal II: Differential survival in a change of habitat // J. Math. Anal. Appl. 1986. V. 115. P.140–154. 
  11. Lu Z., Takeuchi Y. Global asymptotic behaviour in single-species discrete diffusion systems // J. Math. Biol. 1993. V. 32. P. 67–77. 
  12. Cui J., Chen L. The effect of diffusion on the time varying Logistic population growth // Comput. Math. Appl. 1998. V. 36. P. 1–9. 
  13. Takeuchi Y. Global Dynamical Properties of Lotka–Volterra Systems. Singapore: World Scientific, 1996. 308 с. 
  14. Allen L.J. Persistence and extinction in single-species reaction-diffusion models // Bull. Math. Biol. 1983. V. 45. P. 209–227. 
  15. Borodkin F.M., Soboleva S.V. Prognozirovanie chislennosti naseleniya i migracii sistemoj differencial'nyh uravnenij // Matematicheskie metody v sociologii. Novosibirsk: Nauka, 1974. S. 99–145. 
  16. Borodkin F.M., Soboleva S.V., Suharev V.A. Dinamicheskaya model' migracii gorodskogo naseleniya // Matematicheskoe modelirovanie v sociologii (metody i zadachi) / Otv. red. F.M. Borodkin, B.G. Mirkin. Novosibirsk: Nauka. Sib. otd-e. 1977. S. 44–77. 
  17. Soboleva S.V. Demoehkonomicheskie makromodeli migracii sel'skogo naseleniya // Prognozirovanie ehkonomicheskogo i social'nogo razvitiya agrarnogo sektora i APK: sb. nauch. tr. / Pod red. F.M. Borodkina; IEHOPP SO AN SSSR. Novosibirsk, 1981. S. 116–144. 
  18. Soboleva S.V. Demoehkonomicheskie modeli migracii / IEHOPP SO AN SSSR. Novosibirsk, 1982. 61 s.  
  19. Lee R.D. Probabilistic approachs to population forecasting / Eds. Lutz W., Vaupel J., Ahlburg D. Supplement to v. 24. Population and Development Review // Rethinking Population Projection. 1999. P. 156–190. 
  20. Vasil'eva T.P. Matematicheskoe modelirovanie migracionnyh processov v territoriyah: Avtoref. diss. ... kand. fiz.-matem. nauk. Perm'. 2013. 118 s. 
  21. Resin V.I., Popkov YU.S., Darhovskij B.S. Veroyatnostnye tekhnologii v upravlenii razvitiem gorodov. M.: URSS. 2004. 352 c. 
  22. Demidova A.V., Druzhinina O.V., Masina O.N. Issledovanie ustojchivosti modeli populyacionnoj dinamiki na osnove postroeniya stohasticheskih samosoglasovannyh modelej i principa redukcii // Vestnik RUDN. Seriya «Matematika. Informatika. Fizika». 2015. № 3. C. 18–29. 
  23. Demidova A.V., Druzhinina О.V., Jacimovic M., Masina О.N. Construction and analysis of nondeterministic models of population dynamics // Communications in Computer and Information Science (CCIS). Springer, 2016. V. 678. P. 498–510. 
  24. Pugachev V.S., Sinicyn I.N. Teoriya stohasticheskih sistem. M.: Logos, 2000, 2004. 1000 s. [Angl. per. Stochastic Systems. Theory and Applications. Singapore: World Scientific. 2001. 908 p.]. 
  25. Sinicyn I.N., Sinicyn V.I. Lekcii po normal'noj i ehllipsoidal'noj approksimacii raspredelenij v stohasticheskih sistemah. M.: TORUS PRESS, 2013. 488 s. 
  26. Sinicyn I.N., Sinicyn V.I. Analiticheskoe modelirovanie normal'nyh processov v vol'terrovskih stohasticheskih sistemah // Sistemy i sredstva informatiki. 2018. T. 28. № 1. S. 3–15.

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