Russian version English version
Volume 6   Issue 1   Year 2011
Pertsev N.V., Loginov K.K.

Stochastic model of dynamics of biological community in conditions of consumption by individuals of harmful food resources

Mathematical Biology & Bioinformatics. 2011;6(1):1-13.

doi: 10.17537/2011.6.1.


  1. Hallam TG, Clark CE, Lassiter RR. Effects of toxicants on populations: A qualitative approach. I. Equilibrium environment exposure. Ecol. Model. 1983;18:291–304. doi: 10.1016/0304-3800(83)90019-4
  2. Hallam TG, Clark CE, Jordan GS. Effects of toxicants on populations: A qualitative approach. II. First order kinetics. J. Math. Biol. 1983;18:25–37.
  3. Hallam TG, De Luna JL. Effects of toxicants on populations: A qualitative approach. III. Environmental and food chain pathways. J. Theoret. Biol. 1984;109:411–429.
  4. Ma Z, Gui G, Wang W. Persistence and extinction of a population in a polluted environment. Math. Biosci. 1990;101:75–97.
  5. Freedman HI, Shukla JB. Models for the effect of toxicant in single-species and Predator-prey systems. J. Math. Biol. 1991;30:15–30.
  6. Krestin SV, Rozenberg GS. About one of the mechanism of “flowering of water” in flat tape reservoir. Biophysics. 1996;41(3):654
  7. Dubey B. Modelling the effect of toxicant on forestry resources. Indian J. Appl. Math. 1997;28:1–12.
  8. Dubey B, Hussain J. Modelling the interaction of two biological species in a polluted environment. J. Math. Anal. Appl. 2000;246:58–79.
  9. Jinxiao P, Zhen J, Zhien M. Thresholds of Survival for an n-Dimensional Volterra Mutualistic System in a Polluted Environment. J. of Math. Anal. Appl. 2000;252:519–531.
  10. Xiao Y, Chen L. Effects of toxicants on a stage-structured population growth model. Appl. Math. and Comput. 2001;123:63–73.
  11. Mukherjee D. Persistence and global stability of a population in a polluted environment with delay. J. of Biol. Sys. 2002;10(3):225–232.
  12. Liu B, Chen L, Zhang Y. The effects of impulsive toxicant input on a population in a polluted environment. J. of Biol. Sys. 2003;11(3):265–274.
  13. Dubey B, Hussain J. Nonlinear models for the survival of two competing species dependent on resource in industrial environments. Nonlinear Analysis: Real World Applications. 2003;4:21–44. doi: 10.1016/S1468-1218(02)00011-1
  14. Pichugina AN. An integrodifferential model of a population under the effects of pollutants. Sib. Zh. Ind. Mat. 2004;7(4):130–140. (In Russ.)
  15. Karelina RO, Pertsev NV, Construction of two-sided estimates for solutions of some systems of differential equations with aftereffect. Sib. Zh. Ind. Mat. 2005:8(4):60–72. (In Rus.)
  16. Naresh R, Sundar S, Shukla J. Modelling the effect of an intermediate toxic product formed by uptake of a toxicant on plant biomass. Appl. Math. and Comput. 2006;182:151–160.
  17. Feng Z, Liu R, DeAngelis DJ. Plant-herbivore interactions mediated by plant toxicity. Theor. Popul. Biol. 2008;73:449–459.
  18. Li Z, Chen F. Extinction in periodic competitive stage-structured Lotka-Volterra model with effects of toxic substances. J. of Comput. and Appl. Math. 2009;231:143–153.
  19. Pertsev NV, Tsaregorodtseva GE, Pichugina AN. Vestnik Omskogo Universiteta. 2009;2:46–49. (In Russ.)
  20. Pertsev NV and Tsaregorodtseva GE. A mathematical model of the dynamics of a population affected by harmful substances. Journal of Applied and Industrial Mathematics. 2011;5(1):94-103. doi: 10.1134/S199047891101011X
  21. Loginov KK. In: Stokhasticheskie modeli v biologii i predel'nye algebry (Stochastic models in biology and limit algebras): Proceedings of the International conference (2-7 August 2010). Omsk, 2010, pp. 54–55. (In Russ.)
  22. Pichugin BIu, Pertsev NV, Loginov KK. In: Matematicheskaia biologiia i bioinformatika (Mathematical Biology and Bioinformatics): Abstracts of the III International Conference (Pushchino, 10-15 October 2010). Moscow, 2010, pp. 208-209. (In Russ.)
  23. Barucha-Rid AT. Elementy teorii markovskikh sluchainykh protsessov i ikh prilozheniia (Elements of the theory of Markov processes and their applications). Moscow, 1969, p. 512. (In Russ.)
  24. Sobol' IM. Chislennye metody Monte-Karlo (Numerical Monte Carlo methods). Moscow, 1973, p. 311. (In Russ.)
  25. Ermakov SM, Mikhailov GA. Kurs statisticheskogo modelirovaniia (Course of statistical modeling). Moscow, 1976, p. 319. (In Russ.)
  26. Kalinkin AV. Markov branching processes with interaction. Russ. Math. Surv. 2002;57(2):241. (In Russ.) doi: 10.1070/RM2002v057n02ABEH000496
  27. Kalinkin AV, Lange AM, Mastikhin AV, Shaposhnikov AA. Vestnik MGTU imeni N.E. Baumana. 2005;2:53–74.(In Russ.).
  28. Kalinkin AV, Lange AM. In: Stokhasticheskie modeli v biologii i predel'nye algebry (Stochastic models in biology and limit algebras): Proceedings of the International Conference (2-7 August 2010). Omsk, 2010, pp. 40–43. (In Russ.)
  29. Marchenko MA. The program package MONC for distributed computations by Monte Carlo method. Siberian Journal of Numerical Mathematics. 2004;7(1):43–55. (In Russ.)
  30. Pertsev NV, Pichugin BIu. Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta. 2006;2(5):70–77. (Seriia “Vychislitel'nye i informatsionno-telekommunikatsionnye sistemy”). (In Russ.)
Table of Contents Original Article
Math. Biol. Bioinf.
doi: 10.17537/2011.6.1
published in Russian

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


  Copyright IMPB RAS © 2005-2024