COMPUTER MODELING OF STURGEON POPULATION OF THE CASPIAN SEA WITH TWO TYPES OF APERIODIC OSCILLATIONS

Authors

  • A. Yu. Perevaryukha St. Petersburg Institute for Informatics and Automation, St. Petersburg, Russia, Russian Federation

DOI:

https://doi.org/10.15588/1607-3274-2015-1-3

Keywords:

computer model of biological processes, hybrid system, transient chaos, bifurcation, computational experiment

Abstract

The article suggests the original computer model of the life cycle of sturgeon populations of the Caspian Sea, currently included in the «Red
Book» since 2010. In our model was implemented event-stage computing structure that includes continuous and discrete components of the
time. Features of the dynamics of the new model considered by us on the basis of the numerical solution of a finite sequence of the Cauchy
problem for the system of equations describing the subsided of number of individuals in generations. As a result, we obtained the functional
dependence, which be of interest to ichthyologists and which has two local extrema. The possibility of attraction of the trajectory to the two
attractors and the appearance an aperiodic transition regime is established. After the bifurcation of the disappearance of two nontrivial
stationary points arises an interval attractor. For this type of attractor on the Guckenheimer classification is observed the phenomenon of
boundary crisis that for the sturgeon populations is interpreted as an event that threat to their continued existence.

References

Vul Е. B. Feigenbaum universality and the thermodynamic formalism Sinai / Е. B. Vul, K. M. Khanin // Russian Mathematical Surveys. – 1984. – Vol. 39, № 3. – P. 1–40. DOI: 10.1070/ RM1984v039n03ABEH003162 2. Touzeau S. On the stock-recruitment relationships in fish population models / S. Touzeau, J.-L. Gouz // Environmental modeling and Assessment. – 1998. – №3. – P. 87–93. 3. Mikkelsen N. How can the stock recruitment relationship of the Barents Sea capelin (Mallotus villosus) be improved by incorporating biotic and abiotic factors / N. Mikkelsen, T. Pedersen // Polar Research. – 2004. –№ 1. – P. 19–26. 4. Feigenbaum M. J. Universal behavior in nonlinear systems / M. J. Feigenbaum // Physica D. – 1983. – Vol. 7, № 1–3. – P. 16–39. DOI: 10.1016/0167-2789(83)90112-4 5. Perevaryukha A. Yu. Cyclic and unstable chaotic dynamics in models of two populations of sturgeon fish / A. Yu. Perevaryukha // Numerical Analysis and Applications. – 2012. – Vol. 5, № 3. – Р. 254–264. DOI: 10.1134/S199542391203007X 6. Singer D. Stable orbits and bifurcations of the maps on the interval / D. Singer // SIAM journal of applied math. – 1978. – Vol. 35. – P. 260–268. DOI: 10.1137/0135020 7. Guckenheimer J. Nonlinear oscillations, dynamical systems and bifurcation of vector fields / J. Guckenheimer, P. Holmes. – Springer-Verlag, 1983. – 453 p. DOI: 10.1007/978-1-4612-1140-2 8. Vellekoop М. On intervals, transitivity = chaos / М. Vellekoop, R. Berglund // The American Mathematical Monthly. – 1994. – Vol. 101, № 4. – P. 353–355. DOI: 10.2307/2975629 9. Veshchev P. V. Efficiency of natural reproduction of sturgeons in the Lower Volga under current conditions / P.V. Veshchev, G. I. Guteneva, R. S. Mukhanova // Russian Journal of Ecology. – 2012. – Т. 43, № 2. – P. 142–147. DOI: 10.1134/ S1067413612020154 10. Ricker W. E. Stock and recruitment / W. E. Ricker // Journal Fisheries research board of Canada. – 1954. – Vol. 11, № 5. – P. 559–623. DOI: 10.1139/f54-039 11. Paar V. Sensitive dependence of lifetimes of chaotic transient on numerical accuracy for a model with dry friction and frequency dependent driving amplitude / V. Paar, N. Pavin // Modern Physics Letters B. – 1996. – Vol. 10, № 4. – P.153–159. DOI: 10.1142/S0217984996000183 12. Grebogi C. Chaotic attractors in crisis / C. Grebogi, E. Ott, J. A. Yorke // Physical Review Letters. – 1982. – Vol. 48, № 22. – P. 1507–1510. DOI: http://dx.doi.org/10.1103/ PhysRevLett.48.1507 13. Grebogi C. Chaos, strange attractors and fractal basin boundaries in nonlinear dynamics / C. Grebogi, E. Ott, J. A. Yorke // Science. – 1987. – Vol. 238, № 4827. – P. 632-638. DOI: 10.1126/ science.238.4827.632 14. Bruin H. Topological conditions for the existence of absorbing cantor sets / H. Bruin // Transactions of the American mathematical society. – 1998. – Vol. 350, № 6. – P. 2229–2263. DOI: 0002-9947(98)02109-6 15. Minto C. Survival variability and population density in fish populations / C. Minto, R. A. Myers, W. Blanchard // Nature. – 2008. – Vol. 452. – P. 344–348. DOI: 10.1038/nature06605 16. Еремеева Е. Ф. Теория этапности развития и еe значение в рыбоводстве / Е. Ф. Еремеева, А. И. Смирнов // Теоретические основы рыбоводства. – М.: Наука, 1965. – С. 129–138.

Published

2014-10-14

How to Cite

Perevaryukha, A. Y. (2014). COMPUTER MODELING OF STURGEON POPULATION OF THE CASPIAN SEA WITH TWO TYPES OF APERIODIC OSCILLATIONS. Radio Electronics, Computer Science, Control, (1). https://doi.org/10.15588/1607-3274-2015-1-3

Issue

Section

Mathematical and computer modelling