Mathematics · Differential Equations
Consider the system dXdt = β1X(1 − Xk) − c1XY, dYdt = c2XY − α2Y for prey-predator growth of prey, where all constants are positive. Find all the equilibrium points.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(X, Y) = (0, 0), (0, k), (c2/α2, (c1/β1)(1 − α1/(c1k)))
- 2(X, Y) = (0, 0), (k, 0), (α2/c2, (β1/c1)(1 − α2/(c2k)))✓
- 3(X, Y) = (0, 0), (0, k), (α2/c1, (β1/c2)(1 − α2/(c2k)))
- 4(X, Y) = (0, 0), (0, k), (α2/c1, (β1/c2)(1 − α2/(c1k)))
Correct answer
(X, Y) = (0, 0), (k, 0), (α2/c2, (β1/c1)(1 − α2/(c2k)))
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