Question: 4. Consider the logistic equation: 4. Consider the logistic equation: u' =u(1 -u) with u(0) =a. and the following numerical method (a) Show that the

4. Consider the logistic equation:

4. Consider the logistic equation: u' =u(1 -u) with u(0) =a. and the following numerical method (a) Show that the numerical method is consistent with the logistic equation. (b) Find all fixed points of the logistic equation and classify their stability. (c) Find all fixed points of the numerical method and classify their stability. (d) Write a Python function/script to create a bifurcation diagram for this numerical method

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