Next, consider the function f(x,a) = sin(x) =a- x First, set f(a, 0) = a - 1 and show that lim f(a,x)=a-1. x-0 Then, consider the differential equation where a is a real parameter. y(t): =a- sin(y) = f(y,a) y Find the bifurcation point (y*, a*), sketch the bifurcation diagram, and show that the differential equation for y is similar to the differential equation for x by Taylor expanding f(y,a) near the bifurcation point.
Next, consider the function f(x,a) = sin(x) =a- x First, set f(a, 0) = a - 1 and show that lim f(a,x)=a-1. x-0 Then, consider the differential equation where a is a real parameter. y(t): =a- sin(y) = f(y,a) y Find the bifurcation point (y*, a*), sketch the bifurcation diagram, and show that the differential equation for y is similar to the differential equation for x by Taylor expanding f(y,a) near the bifurcation point.
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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can you please show the birufication diagrams here as well as the solutions to the question
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