the description

Characteristic Equation Roots

Fixed points

stable

${\lambda }_1=0.39,{\lambda }_2=0.5$

$q_0=\left(0,0\right)$

stable

${\lambda }_1=0.41,{\lambda }_2=0.5$

$q_1=\left(1,0\right)$

stable

${\lambda }_1=0.4008,{\lambda }_2=0.5$

$q_2=\left(0.5454,0.5454\right)$