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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