Table 10 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 parallel lines

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

Repeller

L.A.S.

Basin of attraction:

${(0,\mathrm{\infty })}^2$ and

positive y-axis

Every soln. on the positive x-axis is unbounded and tends to (∞,0).

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

Repeller

Saddle

Its stable manifold:

Positive y-axis

Every soln. in ${(0,\mathrm{\infty })}^2$ or on the positive x-axis is unbounded and tends to (∞,0) or (∞,c), c>0.

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

There exist infinitely many equilibria along the horizontal line $y=\frac{{\beta }_1-A_1}{C_1}$.