I have the following 2D-ODEs:
$\frac{dx_1}{dt}=k_1-(k_2+k_3)x_1+k_4x_2-k_5x_1x_2^2$
$\frac{dx_2}{dt}=k_3x_1-(k_4+k_6)x_2+k_5x_1x_2^2$
where $k_1=2.9872232$, $k_2=1$, $k_3=1$, $k_4=12.626548$, $k_5=5.6433885$, and $k_6=0.85914091$.
The nonlinear 2D system supports three fixed points:
$P_1=[1, 2.3130],~\lambda_1=-18.8056,~\lambda_2=-0.753234$ (stable node), $P_2=[2.7183, 0.3130],~\lambda_1=-0.951156,~\lambda_2=-5.47861$ (stable node) $P_3=[2.2562, 0.8509],~\lambda_1=-1.16758,~\lambda_2=3.27506$ (unstable, saddle)
I would like to approximate the unstable and stable manifolds of the saddle. Do you have any advice/book/sheet notes in order to approximate such unstable manifold?
Thanks for your attention.
Regards!