Difference Equations in Ecology (justification and application)

Каменев Г.К., Лысенко Н.А., Поляновский В.О.1, Саранча Д.А.

Dorodnicyn Computing Centre FRCCSC of RAS, E-mail:

1Engelhardt Institute of Molecular Biology of RAS, E-mail:

A method of mathematical simulation of environmemtal biological systems, based on comprehensive studies, including a full set of operations, is proposed. This approach was used in the analysis of fluctuations in the number of tundra animals. This made it possible, when simulation tundra populations and communities, to substantiate a set of interrelated mathematical models of varying degrees of detail. Difference equations are considered as simplified models. The relationship of these equations with the original detailed models is traced. On the basis of difference equations, hypotheses are formulated on the leading mechanisms that determine the variations in the numbers of tundra animals (foxes and lemmings). The parameters of the difference equation were identified, based on a series of lemming population numbers in various regions of Russia. A good correlation of one of the parameters of the equation with the absolute maximum temperature in the region is shown. In addition, the mathematical properties of the resulting difference equations are considered. A bifurcation scenario is proposed, in which there are zones of stability with periods varying in the order of the natural series, and zones with more complex modes. The study of transition zones ("ordering chaos") with the help of analytical calculations and computational experiments.

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