state

eigenvalues

Fixed point

stable

$\left|{\lambda }_1\right|=0.6,\left|{\lambda }_2\right|=0.3,\left|{\lambda }_3\right|=0.2$

$p_0=\left(0,0,0\right)$

stable

$\left|{\lambda }_1\right|=0.6,\left|{\lambda }_2\right|=0.2,\left|{\lambda }_3\right|=0.31$

$p_1=\left(1,0,0\right)$

stable

$\left|{\lambda }_1\right|=0.6,\left|{\lambda }_2\right|=0.3,\left|{\lambda }_3\right|=0.2$

$p_3=\left(0,0,1\right)$

stable

$\left|{\lambda }_1\right|=0.6,\left|{\lambda }_2\right|=0.3,\left|{\lambda }_3\right|=0.2$

$p_4=\left(0,0.811966,0.188034\right)$

stable

$\left|{\lambda }_1\right|=0.2,\left|{\lambda }_2\right|=0.6,\left|{\lambda }_3\right|=0.2992$

$p_5=\left(0.461870,0.617581,0.188034\right)$