Landau global oscillator model

In this part, we will study the Landau global oscillator model with a Re =132812.

Once we have the data of the vibration position, we will use the Landau global oscillator model to analysis the physical parameters. The amplification envelopes of the signals have been treated by the Landau global oscillator model (Landau, 1944), Provansal and al (Provansal and al., 1987). Here is the Stuart-Landau equation:
\begin{equation}
\frac{dA}{dt}=\sigma A-\frac{1}{2} l |A|^2 A
\end{equation}

Where A is the complex amplitude of the transverse position in
the flow axis, which is the most significant quantity of the symmetry (varies on time especially for the transition regime); $\sigma$ is the relative growth rate; $l$ is the Landau constant.

Then we have the Landau equation :
\begin{equation}
\frac{d|A|}{dt}=\sigma_r |A|-\frac{1}{2} l_r |A|^2 A
\end{equation}
where $\sigma_r$ is the amplification rate in the linear regime and $l_r$ is the Landau constant in the non-linear regime.