Ex \( \quad x^{\prime}=x(1-x)+0.5 x y \)
\[
\left.y^{\prime}=y(2.5-1.5 y)+-.5 x y\right)
\]
Elassif all equilitrium points.

Answer

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Answer

Equilibrium points: \((x, y) = (0, 0), (1, 0), (0, \frac{5}{3}), (\frac{3}{5}, \frac{3}{5})\)

Steps

Step 1 ：Set \(x' = 0\) and \(y' = 0\): \(x(1 - x) + 0.5xy = 0\) and \(y(2.5 - 1.5y) - 0.5xy = 0\)

Step 2 ：Solve for \(x\) and \(y\): \((1 - x - 0.5y)x = 0\) and \((2.5 - 1.5y - 0.5x)y = 0\)

Step 3 ：Equilibrium points: \((x, y) = (0, 0), (1, 0), (0, \frac{5}{3}), (\frac{3}{5}, \frac{3}{5})\)