Numerical Approximation of Periodic Points For Some Mappings

Islamov, M. I.
Kutlumuratov, R.R.
Ismailov, A. I.

Innovative Technologica: Methodical Research Journal
Vol. 4 No. 2 (2025): June

This study delves into the numerical approximation of periodic points for quadratic mappings, with a particular focus on ecological dynamics represented by the logistic map. We extend the analysis to two-dimensional mappings to capture the interactions between interconnected islands, where parameters reflect living conditions and population dynamics. The investigation involves solving systems of equations to identify points where the period of the mapping equals four, distinguishing them from points with periods equal to two. Approximate solution methods are employed due to the complexity of the equations, facilitating the exploration of periodic orbits and their spectral characteristics through numerical experimentation.