Question: (Subcritical pitchfork) Consider the system x' = rx + x 3 - x 5 , which exhibits a pitchfork bifurcation. a. Find the algebraic expressions

(Subcritical pitchfork) Consider the system x' = rx + x3 - x5, which exhibits a pitchfork bifurcation.

a. Find the algebraic expressions for all teh fixed points as r varies

b. Sketch the vector fields as r varies. Be sure to indicate all the fixed points and their stability

c. Calculate rs, the parameter value at whcih the nonzero fixed points are born in a saddle-node bifurcation

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