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Consider the system dx/dt = rx + x^3 - x^5, which exhibits a subcritical pitchfork bifurcation.

a) Find algebraic expressions for all the fixed points.

b) Calculate r_s, the parameter value at which the nonzero fixed points are born in a saddle-node bifurcation.

The attempt at a solution

x* = 0 and x* = ±√½±½√4r+1.

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# Homework Help: Subcritical Pitchfork Bifurcation

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