(Solution) - Analyze the stability of the positive equilibrium in the model -(2025 Original AI-Free Solution)

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Analyze the stability of the positive equilibrium in the model from Exercise 44 when ? = 4, the point where the bifurcation occurs.
Right at a bifurcation point, the stability theorem fails because the slope of the rate-of-change function at the equilibrium is exactly zero. In each of the following cases, check that the stability theorem fails, and then draw a phase-line diagram to find the stability.