We are given the following nonlinear system ,
$\frac{dI}{dt} = J \\ \frac{dJ}{dt} = -0.1\left(I^{3}(C - C_{0}\right)I - F - 0.2 J\\ \frac{dC}{dt} = \epsilon\left(F + \frac{C}{\sqrt{F^2 + C^2}}\left(1-\left(\frac{F}{\alpha}\right)^2-\left(\frac{C}{\beta}\right)^2\right)\right)\\ \frac{dF}{dt} = \epsilon\left(-0.1 C + \frac{F}{\sqrt{F^2 + C^2}}\left(1-\left(\frac{F}{\alpha}\right)^2 - \left(\frac{C}{\beta}\right)^2\right)\right) $
Where $\epsilon << 1$.
The critical manifold would be when,
$-a_{1}\left(I^{3}(C - C_{0}\right)I - a_{2}F - \gamma J = 0$
What would the method to find the attractive and repelling parts of the critical manifold?