Folded Saddle-nodes and Their Normal Form Reduction in a Neuronal Rate Model∗
نویسندگان
چکیده
The paper investigates the existence of folded singularities in a dynamical system of two fast and two slow equations. The normal form of the system near its fold curve is constructed. Then it is used to determine the analytical conditions satisfied by a folded singularity. In particular, we find that there is a parameter region where folded saddle-nodes of type II exist. In the neighborhood of those points the system possesses a stable folded node and an unstable true equilibrium, and the local dynamics is complex. MSC 2010: 37G05, 34E13, 92C20 keywords: inhibitory neural networks, folded singularities, canards
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تاریخ انتشار 2011