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lecture_8 (dragged) 2

lecture_8 (dragged) 2 - y = y t tend to a stable...

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MA 36600 LECTURE NOTES: FRIDAY, JANUARY 30 3 Example. As an example, consider the function f ( y ) = r y (1 y ) = r y y 2 = f ( y ) = r (1 2 y ) . The equilibrium solutions are y L = 0 and y L = 1. We have f (0) = r > 0 and f (1) = r < 0. Hence y L = 0 is an unstable equilibrium solution, while y L = 1 is a stable equilibrium solution. Figure 1 contains a plot of f ( y ) vs. y . Philosophically, “most” solutions
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Unformatted text preview: y = y ( t ) tend to a stable equilibrium solution y L . Figure 1. Plot of f ( y ) = r y (1 − y )-0.08 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 1.04 1.12-0.32-0.24-0.16-0.08 0.08 0.16 0.24 0.32 0.4 0.48 Decreasing f'(y) < 0 Increasing f'(y) > 0...
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