# User:Eugene M. Izhikevich/Proposed/Saddle-node bifurcation on invariant circle

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Figure 1: Saddle-node bifurcation on an invariant circle ($$\beta$$ is a bifurcation parametr).

Saddle-node bifurcation on invariant circle, also known as SNIC or SNLC (saddle-node on limit cycle) bifurcation, occurs when the center manifold of a saddle-node bifurcation forms an invariant circle, as in Figure 1. Such a bifurcation results in (dis)appearance of a limit cycle of an infinite period. It plays an important role in computational neuroscience, where it is exhibited by Class 1 excitable systems (such as cortical pyramidal neurons).