Consider the logistic map Derive analytically an expression for the fixed point x* given by x* =
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Consider the logistic map
Derive analytically an expression for the fixed point x* given by x* = ƒ(x*) and the point xtan for which ƒ(x) has a tangent parallel to the identity, i.e. ƒ(xtan) = 1. Use the expression in Eq. (12.40) to estimate the number of iterations needed to pass through the bottleneck.
Equation (12.40)
Choose r = 1 + Δ . For Δ = 0.1,0.01 and 0.001, numerically iterate the map and determine the number of iterations, T, needed to go from x(0) = 10−5 to X(T) = x* ± 10−5; compare your results with the results obtained from Eq. (12.40).
Equation (12.40)
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Related Book For
Complexity Science The Study Of Emergence
ISBN: 9781108834766
1st Edition
Authors: Henrik Jeldtoft Jensen
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