Table 9 Global behavior of solutions when ${\mathit{\beta }}_{\mathbf{1}}\mathbf{-}{\mathit{A}}_{\mathbf{1}}\mathbf{>}\mathbf{0}$ and ${\mathit{\gamma }}_{\mathbf{2}}\mathbf{-}{\mathit{A}}_{\mathbf{2}}\mathbf{>}\mathbf{0}$ when ${\mathit{E}}_{\mathbf{1}}$ and ${\mathit{E}}_{\mathbf{2}}$ are respectively pairs of perpendicular and transversal lines

$C_2({\beta }_1-A_1)>C_1({\gamma }_2-A_2)$

Repeller

Saddle

Its stable manifold:

Positive y-axis

–

$C_2({\beta }_1-A_1)=C_1({\gamma }_2-A_2)$

Repeller

Saddle

Its stable manifold:

Positive y-axis

Basin of attraction:

(0,∞)×(b,∞), where ${\mathcal{E}}_2=(0,b)$

Note: Solns. in (0,∞)×(0,b)⟶(∞,0)

–

$C_2({\beta }_1-A_1)<C_1({\gamma }_2-A_2)$

Repeller

L.A.S.

Basin of attraction:

Region above an increasing curve $\mathcal{C}$

Saddle

Its stable manifold:

The increasing curve $\mathcal{C}$

Note: Solns. in the region below $\mathcal{C}⟶(\mathrm{\infty },0)$