Conference publications


XXIII conference

Deterministic chaos in population dynamics: mathematical modeling vs reality

Medvinsky A.B., Nurieva N.I., Rusakov A.V.

Institute of Theoretical & Experimental Biophysics, Russian Academy of Sciences, Institutskaya str. 3, Pushchino, Moscow Region, 142290 Russia

1 pp. (accepted)

In this paper, we based on the analysis of data obtained during the field observations, show that planktonic communities in the Naroch lakes (Belarus) demonstrate a chaotic behavior far from the edge of chaos. Namely, with the use of the recurrence quantification analysis [1] we show that the horizon of predictability of the plankton dynamics is of around 2.5 months, which allows [2] an assessment of the dominant Lyapunov exponent. Corresponding numerical values of the Lyapunov exponent are close to 0.4. Such values of the Lyapunov exponent lay out of the narrow interval between -0.1 and +0.1 characteristic of living at the edge of chaos. Furthermore, with the use of the recurrence quantification analysis [1] we have found that the second order Renyi entropy characteristic of both phytoplankton and zooplankton in the Naroch lakes are in many cases considerably greater than corresponding values of the dominant Lyapunov exponent. It imples that the plankton dynamics can be characterized by at least ywo physical degrees of freedom. Therefore, the description of irregular changes in plankton abundance can in these cases require a four- or higher-dimensional phase space [3]. However, it is possible that the heterogeneity of the habitat is able to neutralize the manifestations of chaos [4]. The results shown here are published, in particular, in [5].

1. Marwan N., Romano M.C., Thiel M., Kurths J., / Physics Reports, 2007, V. 438, p. 237-329.

2. Boffetta G., Cencini M., Falcioni M., Vulpiani A. / Physics Reports, 2002, V. 356, p. 367-474.

3. Takens F. / Lecture Notes in Mathematics, 1981, V. 898, p. 336-381.

4. Medvinsky A.B., Bobyrev A.E., Burmensky V.A., Kriksunov E.A., Nurieva N.I., Rusakov A.V. / Russian Journal of Numerical Analysis and Mathematical Modelling, 2015, V. 30, p. 55-70.

5. Medvinsky A.B., Adamovich B.V., Chakraborty A., Lukyanova E.V., Mikheyeva T.M., Nurieva N.I., Radchikova N.P., Zhukova T.V. / Ecological Complexity, 2015, V. 23, p. 61-67.

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