(1) Consider the logistic map Lu(x) = ux(1-x), x = [0, 1]. (a)Show that for 0...

 

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(1) Consider the logistic map Lu(x) = ux(1-x), x = [0, 1]. (a)Show that for 0 <μ< 4, the fixed point x = 0 has no eventual fixed points other than x = 1. (b)Show that for 1 <u≤ 2, the fixed point x = 1 - 1/μ only has x = 1/μ as an eventual fixed point, but this is not the case for 2 <μ< 3. (c)Determine whether logistic family undergoes a bifurcation of fixed points as u varies in (0, 4]. If so, sketch the bifurcation diagram. NOTE: Use algebraic and graphical analysis in each part. Do not write a tale. (1) Consider the logistic map Lu(x) = ux(1-x), x = [0, 1]. (a)Show that for 0 <μ< 4, the fixed point x = 0 has no eventual fixed points other than x = 1. (b)Show that for 1 <u≤ 2, the fixed point x = 1 - 1/μ only has x = 1/μ as an eventual fixed point, but this is not the case for 2 <μ< 3. (c)Determine whether logistic family undergoes a bifurcation of fixed points as u varies in (0, 4]. If so, sketch the bifurcation diagram. NOTE: Use algebraic and graphical analysis in each part. Do not write a tale.