SOME PROPERTIES OF TWO DIMENSIONAL QUADRATIC MAPPINGS
Abstract
This paper has presented a thorough exploration of quadratic mappings within two-dimensional dynamical systems, employing a novel geometric approach known as graphical analysis. Through this method, we have gained valuable insights into the behavior of orbits, fixed points, periodic cycles, and bifurcation phenomena inherent in quadratic mappings. The graphical analysis procedure outlined in this paper offers an intuitive and visually appealing way to understand the dynamics of complex systems. By superimposing the graphs of relevant functions, we have been able to discern patterns, predict behaviors, and uncover the underlying structure of quadratic mappings
References
[1] Seytov, Sh.J., Narziyev, N.B., Eshniyozov, A.I., Nishonov, S.N. The algorithms for developing computer programs for the sets of Julia and Mandelbrot. AIP Conference Proceedings, 2023, 2789, 050021.
[2] Seytov, S.J., Eshniyozov, A.I., Narziyev, N.B. Bifurcation Diagram for Two Dimensional Logistic Mapping. AIP Conference Proceeding, 2023, 2781, 020076.
[3] Seytov, S.J., Nishonov, S.N., Narziyev, N.B. Dynamics of the Populations Depend on Previous Two Steps. AIP Conference Proceedings., 2023, 2781, 020071.
[4] Seytov, S.J., Sayfullayev, B.Sh., Anorbayev, M.M. Separating a Finite System of Points from each Other in Real Euclidean Space AIP Conference Proceedings., 2023, 2781, 020043.
[5] Seytov, S.J., Eshmamatova, D.B. Discrete Dynamical Systems of Lotka–Volterra and Their Applications on the Modeling of the Biogen Cycle in Ecosystem. Lobachevskii Journal of Mathematics., 2023, 44(4), pp. 1471–1485.
[6] Eshmamatova, D.B., Seytov, S.J., Narziev, N.B. Basins of Fixed Points for Composition of the Lotka–Volterra Mappings and Their Classification. Lobachevskii Journal of Mathematics., 2023, 44(2), pp. 558–569
[7] Ganikhodzhaev, R.N., Seytov, Sh.J. Coexistence chaotic behavior on the evolution of populations of the biological systems modeling by three dimensional quadratic mappings Global and Stochastic Analysis., 2021, 8(3), pp 41–45.
[8] Ganikhodzhayev, R., Seytov, S. An analytical description of mandelbrot and Julia sets for some multi-dimensional cubic mappings/ AIP Conference Proceedings., 2021, 2365, 050006.
