In the interval [0,1] function sr(x) = r sin πx behaves similar to logistic function hμ(x) = μx(1‐ x). We prove that for every r > there exists subset ? ⊂ [0,1] such that sr: ? → ? is a chaotic function. Since the logistic function is chaotic in another subset of [0,1] but both functions have similar graphs in [0,1] we conclude that it can lead to errors in practice.
Bula, I., & Vintere, A. (2006). On the population model with a sine function. Mathematical Modelling and Analysis, 11(1), 35-40. https://doi.org/10.3846/13926292.2006.9637300
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there exists subset ? ⊂ [0,1] such that sr : ? → ? is a chaotic function. Since the logistic function is chaotic in another subset of [0,1] but both functions have similar graphs in [0,1] we conclude that it can lead to errors in practice.