Compare the initial bifurcation cascade

Reference no: EM13924475

Q1) Show that the attractor A of the IFS f = { 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] defined by f(x) = 27/4 μx²( 1-x) with that of the logistic family g: [0,1] ->. [0,1] defined by g(x) = 4 μx( 1-x) , where in each case μ ∈ [0,1]. Identify the parameter values for which there is a single attractive fixedpoint, 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.

Reference no: EM13924475

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