Search for and stabilization of unstable saddle cycles in the Lorenz system (Q1874812)

The author proves the existence of an unstable limit cycle \(C_0\) (eight-shaped) in the Lorenz system for the parameter values \(r=17, \sigma=10, b=8/3\). The algorithm of \textit{N. A. Magnitskii} and \textit{S. V. Sidorov} [Differ. Equ. 37, 1568--1579 (2001; Zbl 1016.37016)] was used to compute this limit cycle. Additionally, the stabilization of the cycle is performed using the method developed by the same authors [Differ. Equ. 34, 1501--1509 (2001; Zbl 0977.93036)].