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Use linear stability analysis to classify the fixed points of the following system. $f(x)=ax-x^3 $ where a can be positive, zero or negative.

I have found that for $a>0$ we have $2$ fixed points For $a=0$ only $x=0$ is a fixed point at which it is stable

  • I don't understand how the solution for $a<0. $

  • I am not sure why $x=0$ is only the solution

any help will be appreciated thank u!

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    The rhs is a 3rd degree polynomial, so expect 3 fixed points in general. Think complex...2012-10-30

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