Studying the Recurrent Sequence Generated by Power Function using QUATTRO-20

Abstract

We presented the bifurcational diagram of power function Fi(x) = r·x·(1 – x^2) which could be treated as first approximation of trigonometric function F(x) = r·x·cos x. Using second composite Fi^2(x) in analytical form and solving 8-th degree polynomial equation bifurcational diagram with period doubling 1, 2, 4 was obtained and attractors were established. Analytical solutions of expressions x = Fi^2(x) allows us to establish the fixed point attractors and periodic attractors in interval (-V5,V5). Bifurcation diagram obtained analytically was compared with its aproximate analogue Finite State diagram. ‍