Theory and Modern Applications
Table 2 Summary of the existence and local stability conditions of each equilibrium points of system (1). The results are based on those of system (2) as stated in Theorems 3.1, 3.3, 3.5, and 3.7
From: Optimal control problem arises from illegal poaching of southern white rhino mathematical model
Extinction equilibrium \(\mathcal{E}_{1} = (0,0,0,0)\) | Hunter-free equilibrium \(\mathcal{E}_{2} = (N_{1},N_{2},0,0)\) | Coexistence equilibrium \(\mathcal{E}_{3} = (N_{1},N_{2},N_{3},M)\) | |
|---|---|---|---|
Existence | ✓ | \(\mathcal{R}_{1}^{*}>1\) | \(\mathcal{R}_{2}^{*}>1\) |
Local stability | \(\mathcal{R}_{1}^{*}<1\) | \(\mathcal{R}_{2}^{*}<1\) | \(\mathcal{R}_{2}^{*}>1\) |