Consider the map given by [x_{n+1}=x_{n} e^{alphaleft(1-x_{n} ight)}] used to study population growth limited by disease. Analyze
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Consider the map given by
\[x_{n+1}=x_{n} e^{\alpha\left(1-x_{n}\right)}\]
used to study population growth limited by disease. Analyze the system as done for the logistic map in the text, identifying the onset of chaos and bifurcations, if any. Consider in particular values of \(\alpha=1.5,2,2.7\).
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