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The shape of phase-resetting curves in oscillators with a saddle node on an invariant circle bifurcation. (English) Zbl 1268.92016
Summary: We introduce a simple two-dimensional model that extends the Poincaré oscillator so that the attracting limit cycle undergoes a saddle node bifurcation on an invariant circle (SNIC) for certain parameter values. Arbitrarily close to this bifurcation, the phase-resetting curve (PRC) continuously depends on parameters, where its shape can be not only primarily positive or primarily negative but also nearly sinusoidal. This example system shows that one must be careful inferring anything about the bifurcation structure of the oscillator from the shape of its PRC.

MSC:
92B25 Biological rhythms and synchronization
37N25 Dynamical systems in biology
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