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.

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