Problem
\[ \begin{array}{l} \frac{d x}{d t}=\beta x\left(1-\frac{x}{k}\right)-c_{1} x y \\ \frac{d y}{d t}=-\alpha y+c_{2} x y \end{array} \] Classify all equilibrium point of the following
Solution
Step 1 ：\(0 = \beta x\left(1-\frac{x}{k}\right)-c_{1} xy \)
Step 2 ：\(0 = -\alpha y+c_{2} xy \)
Step 3 ：\(x = 0, y = 0 \) or \(x = k, y = \frac{\alpha}{c_{2}} \) or \(y= \frac{\beta}{c_{1}}x\left(1 - \frac{x}{k}\right) \)
