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For each of the following parametrized family of differential equations plot phase lines for λ = -2,-1,0, 1, 2, find any bifurcation values, and sketch the bifurcation diagram. (a) y' = x - y².

For each of the following parametrized family of differential equations plot phase lines for λ = -2,-1,0, 1, 2, find any bifurcation values, and sketch the bifurcation diagram. (a) y' = x - y².

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 4CR
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Help with parts a through e, having some difficulty with the phase lines.

1.7.5 Exercises 1. For each of the following parametrized family of differential equations, plot phase lines for λ = -2, -1,0, 1, 2, find any bifurcation values, and sketch the bifurcation diagram. (a) y' = x - y². (b) y'= Ay² - 1 for > € R. (c) y'= λ- 2y + y². (d) y'= (A-4y²)y. (e) y'= (Ay¹¹)y.
Transcribed Image Text:1.7.5 Exercises 1. For each of the following parametrized family of differential equations, plot phase lines for λ = -2, -1,0, 1, 2, find any bifurcation values, and sketch the bifurcation diagram. (a) y' = x - y². (b) y'= Ay² - 1 for > € R. (c) y'= λ- 2y + y². (d) y'= (A-4y²)y. (e) y'= (Ay¹¹)y.
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