$\alpha =\beta =\mu =1$

$\begin{array}{l}{U}_{1,2}=\pm \sqrt{\frac{-1+i\sqrt{3}}{2}}\\ U_{3,4}=\pm \sqrt{\frac{-1-i\sqrt{3}}{2}}\end{array}$

−1

−1

1

−1

Spirals

Spirals

Spirals

Asymptotically stable

Unstable

Unstable

$\alpha =1,\beta =\mu =-1$

$\begin{array}{l}{U}_{1,2}=\pm \sqrt{\frac{-1-i\sqrt{5}}{2}}\\ U_{3,4}=\pm \sqrt{\frac{-1+i\sqrt{5}}{2}}\end{array}$

−1

−1

1

−1

Saddles

Saddles

Saddles

Saddles

Unstable

Unstable

Unstable

Unstable

$\alpha =1,\beta =-1,\mu =0.01$

$\begin{array}{l}{U}_{1,2}=\pm \sqrt{\frac{-1+\sqrt{0.96}}{0.02}}\\ U_{3,4}=\pm \sqrt{\frac{1-\sqrt{0.96}}{0.02}}\end{array}$

−1

−1

1

−1

Spirals

Spirals

Saddle

Asymptotically stable

Unstable

Unstable

Unstable

Unstable

$\alpha =-1,\beta =\mu =1$

$\begin{array}{l}{U}_{1,2}=\pm \sqrt{\frac{-1+\sqrt{5}}{2}}\\ U_{3,4}=\pm \sqrt{\frac{-1-\sqrt{5}}{2}}\end{array}$

−1

−1

1

−1

Spirals

Spirals

Spirals

Spirals

Asymptotically stable

Unstable

Asymptotically stable

Unstable

$\alpha =-1,\beta =1,\mu =-0.02$

$U_{1,2}=\pm \sqrt{\frac{1-\sqrt{0.92}}{0.04}}$

−1

−1

1

−1

Spirals

Saddles

Saddles

Saddles

Asymptotically stable

Unstable

Unstable

Unstable