Theory and Modern Applications
Table 1 Properties of \((x_{4},y_{4})\)
From: Identifying weak focus of order 3 in a Leslie–Gower prey–predator model with prey harvesting
Parameter conditions | Properties | ||
|---|---|---|---|
\(0<\beta <\frac{1}{2}\) | \(0<\delta <\frac{1}{2}-\beta \) | \(0<\varepsilon <\varepsilon _{1}\) | stable node or focus |
\(\varepsilon =\varepsilon _{1}\) | center type | ||
\(\varepsilon _{1}<\varepsilon <\frac{\beta }{4(\beta +\delta )}\) | unstable node or focus | ||
\(0<\beta <\frac{1}{2}\) | \(\delta \geq \frac{1}{2}-\beta \) | \(0<\varepsilon <\frac{\beta }{4(\beta +\delta )}\) | stable node or focus |
\(\beta \geq \frac{1}{2}\) | δ>0 | \(0<\varepsilon <\frac{\beta }{4(\beta +\delta )}\) | stable node or focus |