Bifurcation

Transcritical bifurcation

The transcritical bifurcation occurs when one node collides and passes over another, in the process swapping stabilities.

Flows

The canonical form is

with fixed points 𝑥∗1 =0 and 𝑥∗2 =𝜇. With this setup,

• 𝜇 <0 has 𝑥∗1 =0 stable and 𝑥∗2 =𝜇 unstable
• 𝜇 =0 has 𝑥∗1 =𝑥∗2 =0 non-hyperbolic
• 𝜇 >0 has 𝑥∗1 =0 unstable and 𝑥∗2 =𝜇 stable

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