Equilibria Stability condition Equilibrium nature
\(E_{0}\) No condition Unstable
\(E_{1}\) \(\frac{r_{2}}{\beta}<r_{1}<\frac{d}{c_{1}\varepsilon}\) LAS
\(E_{2}\) \(\frac{r_{1}}{\alpha}<r_{2}<\frac{d}{c_{2}\mu}\) LAS
\(E_{12}\) \(\alpha\beta<1,\mathrm{\ }d>c_{1}\varepsilon{\overset{\overline{}}{x}}_{1}+c_{2}\mu{\overset{\overline{}}{x}}_{2}.\) LAS
\(E_{13}\) \(\frac{r_{2}}{1+k_{2}\hat{y}}<\ \beta{\hat{x}}_{1}+\mu\hat{y}\) LAS
\(E_{23}\) \(\frac{r_{1}}{1+k_{1}\tilde{y}}<\ \alpha{\tilde{x}}_{2}+\varepsilon\tilde{y}\) LAS
\(E^{*}\) \(4p_{1}p_{2}>{(p_{1}\alpha+p_{2}\beta)}^{2}\ \) LAS
\(E^{*}\) \(4c_{1}c_{2}>{(c_{1}\alpha+c_{2}\beta)}^{2}\) and det A > 0 GAS