Benchmark solution ===================== We are interested in the calculation of periodic solutions of the system thus characterizing the non-linear mode. Calculation method ------------------ To solve the system, we use the EHMAN [:ref:`1 <1>`] method. We try to follow the branch of periodic solutions starting from the first mode of the underlying linear system. Reference quantities and results ----------------------------------- The reference quantities chosen are the frequency-energy pair and the stability of the periodic solution obtained. A periodic solution is found for the frequency-energy pair such as: :math:`5.2\mathit{Hz}