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Theory and Modern Applications

Table 4 Result of stable equilibrium points for autonomous simulation with various values of parameter \(\alpha ^{*}\)

From: Optimal control problem arises from illegal poaching of southern white rhino mathematical model

Cases

\(\mathcal{R}_{1}^{*}\)

\(\mathcal{R}_{2}^{*}\)

Stable equilibrium

Type

\(N_{1}\)

\(N_{2}\)

\(N_{3}\)

M

\(\alpha ^{*}=\frac{1}{11}\)

0.9803

0.8911

0

0

0

0

Extinction \((\mathcal{E}_{1})\)

\(\alpha ^{*}=\frac{1}{7}\)

1.0638

0.9669

8.94

51.06

0

0

Hunter-free \((\mathcal{E}_{2})\)

\(\alpha ^{*}=\frac{1}{3}\)

1.1628

1.0569

6.39

80.13

0.09

2.43

Coexistence \((\mathcal{E}_{3})\)