Theory and Modern Applications
Table 1 The existence and stability of equilibria of system (1.3), where \(\gamma<1-\delta\beta \)
Qualifications | Equilibria & Stability | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
\(E_{0}\) | \(E_{1}\) | \(E_{21}\) | \(E_{22}\) | \(E_{23}\) | \(E_{23^{*}}\) | \(E_{31}\) | \(E_{32}\) | \(E_{33}\) | \(E_{33^{*}}\) | |
0<α<γ − γδβ | saddle | unstable | – | – | unstable | – | – | – | stable | – |
α = γ − γδβ | saddle | unstable | – | – | unstable | – | – | – | – | stable |
γ − γδβ<α<γ | saddle | stable | – | – | unstable | – | – | unstable | stable | – |
α = γ | saddle | stable | – | – | – | unstable | – | unstable | stable | – |
\(\gamma<\alpha<\alpha_{2}\) | saddle | stable | – | unstable | unstable | – | – | unstable | stable | – |
\(\alpha=\alpha_{2}\) | saddle | stable | – | unstable | unstable | – | unstable | – | – | – |
\(\alpha_{2}<\alpha<\alpha_{1}\) | saddle | stable | – | unstable | unstable | – | – | – | – | – |
\(\alpha=\alpha_{1}\) | saddle | stable | unstable | – | – | – | – | – | – | – |
\(\alpha_{1}<\alpha\) | saddle | stable | – | – | – | – | – | – | – | – |