with finite values of $w_+$ and $w_-$ are referenced in the appendix. Following the same reasoning as for Bianchi type $II$ model, the only set of equilibrium points compatible with an isotropic stable state is $(x_{+},x_{-},y,z,w_+,w_-)=(0,0,\pm \sqrt{3-\ell^2}(6\sqrt{2})^{-1},\ell/6,0,0)$, implying that $\ell^2<3$. It is equivalent to the points found for Bianchi type $II$ model and, for the same reasons, $\ell$ have to tend to a constant with no limit cycle. Another interesting set of points is given by $(x_{+},x_{-},y,z,w_\pm,w_\pm)=((\ell^2-1)(\ell^2+8)^{-1},\pm\sqrt{3}(\ell^2-1)(\ell^2+8)^{-1},\pm \sqrt{12-3\ell^2}\left[2(\ell^2+8)\right]^{-1},3\ell(2\ell^2+16)^{-1},0,\pm\sqrt{-\ell^4+5\ell^2-4}\left[2(\ell^2+8)\right]^{-1})$. However, in this case $x_\pm\rightarrow 0$ only if $\ell^2\rightarrow 1$ and we recover the values of the previous set of points for this particular limit of $\ell^2$ which does not allow isotropisation as it will be shown below. Other sets exist but are complex valued and can thus be discarded. At last, as for Bianchi type $II$ model, let us show that the set of equilibrium points such that $(y,w_+,w_-)=(0,0,0)$ implies that $x_\pm$ do not vanish.\
In this case we deduce from (\[eq52\]-\[eq62\]) that $w_\pm$ behave as $e^{-2\Omega}$ and thus isotropy would arise when $\Omega\rightarrow +\infty$. Then, using the definition (\[var41\]) for $w_\pm$, we derive that $H$ should be a constant near isotropy and, considering equations (\[ppp\]-\[pmp\]), we find that asymptotically $\dot{p}_\pm$ 