For the canonical form of the transcritical bifurcation where u is a real parameter d dt x(t) = Mx = μx − x², determine the local stability of any equilibria, and sketch the bifurcation diagram. Next, consider the differential equation —y(t) = Ay² (1 − 2)y = ƒ (λ, y), dt where is a real parameter. Find the bifurcation point (y*, 2*), sketch the bifurcation diagram, and show that the differential equation for y is similar to the differential equation for x by Taylor expanding f(x,y).
For the canonical form of the transcritical bifurcation where u is a real parameter d dt x(t) = Mx = μx − x², determine the local stability of any equilibria, and sketch the bifurcation diagram. Next, consider the differential equation —y(t) = Ay² (1 − 2)y = ƒ (λ, y), dt where is a real parameter. Find the bifurcation point (y*, 2*), sketch the bifurcation diagram, and show that the differential equation for y is similar to the differential equation for x by Taylor expanding f(x,y).
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
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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