CDS - Subcritical Pitchfork Bifurcation

Remember:

Subcritical Pitchfork Bifurcation:

• $\mu <{\mu }^{\ast }$ : $x_1^{\ast }$ is stable, $x_2^{\ast }$ and $x_3^{\ast }$ are unstable
• $\mu >{\mu }^{\ast }$ : $x_1^{\ast }$ is unstable, $x_2^{\ast }$ and $x_3^{\ast }$ disappear.
• $\mu ={\mu }^{\ast }$ : $x_1^{\ast }$, $x_2^{\ast }$ and $x_3^{\ast }$ coincide.

~Ex.:

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• A similar “sign-switched” case of the previous one.

• This is called the “Subcritical Pitchfork Bifurcation”