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.
Reference26 articles.
1. 1. Bruno Gonpe Tafo, J.; Nana, L.; Tabi, C. B.; Kofané, T. C. (2020) Nonlinear Dynamical Regimes and Control of Turbulence through the Complex Ginzburg-Landau Equation - Research Advances in Chaos Theory IntechOpen - doi:10.5772/intechopen.88053.
2. 2. Tzamal- Odysseas, M. (2014) Energy transfer and dissipation in nonlinear oscillators. PhD theses - Aristotle University of Thessaloniki, Greece, 2014. 3. Elaydi, S. (2005) An introduction to difference equations 3rd ed. - Springer Science: Business Media, Inc., 2005.
3. A First Course in Chaotic Dynamical Systems;Devaney;Theory and Experiment 2nd Edition - Taylor & Francis Group LLC,2020
4. 5. Chen, Y.; Qian, Y.; Cui, X. (2022) Time series reconstructing using calibrated reservoir computing - Scientific Reports 12 (2022) 16318 - https://doi.org/10.1038/s41598-022-20331-3
5. 6. Tronci, S.; Giona, M.; Baratti, R. (2003) Reconstruction of chaotic time series by neural models: a case study - Neurocomputing 55 (2003)581-591 - https://doi.org/10.1016/S0925-2312(03)00394-1.