Parameter region | ${\mathcal{E}}_{\mathbf{0}}$ | ${\mathcal{E}}_{\mathbf{1}}$ | ${\mathcal{E}}_{\mathbf{2}}$ | ${\mathcal{E}}_{\mathbf{3}}$ |
---|---|---|---|---|
${\beta}_{1}-{A}_{1}<0$
${\gamma}_{2}-{A}_{2}<0$ |
G.A.S. Basin of attraction: ${[0,\mathrm{\infty})}^{2}$ | – | – | – |
${\beta}_{1}-{A}_{1}>0$
${\gamma}_{2}-{A}_{2}\le 0$ |
Saddle Its stable manifold: Positive y-axis |
L.A.S. Basin of attraction: ${(0,\mathrm{\infty})}^{2}$ and positive x-axis | – | – |
${\beta}_{1}-{A}_{1}\le 0$
${\gamma}_{2}-{A}_{2}>0$ |
Saddle Its stable manifold: Positive x-axis | – |
L.A.S. Basin of attraction: ${(0,\mathrm{\infty})}^{2}$ and positive y-axis | – |
${\beta}_{1}-{A}_{1}>0$
${\gamma}_{2}-{A}_{2}>0$ | Repeller |
Saddle Its stable manifold: Positive x-axis |
Saddle Its stable manifold: Positive y-axis |
L.A.S. Basin of attraction: ${(0,\mathrm{\infty})}^{2}$ |