4. Consider the system (dot{x} = rx + x^3 - x^5), where (r in mathbb{R}) is a parameter. (a) Find algebraic expression for all of the fixed points as r is varied. (b) Sketch all possible phase portraits as r is varied. (c) Sketch the bifurcation diagram for this problem. In this bifurcation diagram, determine what types of bifurcations occur. (d) Calculate the explicit values for all of the bifurcation points in this problem.
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