Saddle-node bifurcation on invariant circle

• Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia

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).

Sponsored by: Eugene M. Izhikevich, Editor-in-Chief of Scholarpedia, the peer-reviewed open-access encyclopedia