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In this paper we consider properties of the difference equations (discrete mappings) obtained in the study of the population dynamics of lemmings. A bifurcation scenario is proposed for obtained equations. Certain stability zones appear under this scenario with periods varying in order of natural series and also zones with more complicated modes. The study of transitional zones (‘ordering of the chaos’) is performed with the use of analytic calculations and computational experiments. Numerical analysis of mappings uses the methods of approximation of implicitly specified sets allowing us to construct and visualize sets of ‘resonance’ parameters including the front of the so-called singularity of ‘blue sky’.

From chaos to order. Difference equations in one ecological problem