Logistic map
Course:- Mathematics
Reference No.:- EM13286

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Q1) Show that the attractor A of the IFS ƒ = { R2 ( x/2, y/2), ( x+1 /2, y/2), (x/4, y+3/ 4)} is neither connected nor disconnected.

Q2) Compare the initial bifurcation cascade for f: [0,1] → [0,1] de?ned by f(x) = 27/4 μx2( 1-x) with that of the logistic family g: [0,1] → [0,1] de?ned by g(x) = 4 μx( 1-x) , where in each case μ ε [0,1]. Identify the parameter values for which there is a single attractive ?xedpoint, and the value at which it transfers stability to an attractive 2-cycle. In each case, at which value, as the paramater increases, does the attractive 2-cycle lose its stability.

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