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Consider the spruce budworm model. A bifurcation occurs approximately at the point (k, r) = (9.57, 0.4). Sketch the graph of the curve X/(1+X^2) and

Consider the spruce budworm model.

A bifurcation occurs approximately at the point (k, r) = (9.57, 0.4). Sketch the graph of the curve X/(1+X^2) and line r(1 X/K) for this situation. Make sure to label your axes. Then use the over-under method to draw the associated phase portrait, indicating the stability of the equilibrium point(s).

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