Analysis of neural excitability and oscillations
Methods in neuronal modeling
Synchrony in excitatory neural networks
Neural Computation
Type i membranes, phase resetting curves, and synchrony
Neural Computation
Synaptic and intrinsic determinants of the phase resetting curve for weak coupling
Journal of Computational Neuroscience
Synchronization of delayed coupled neurons in presence of inhomogeneity
Journal of Computational Neuroscience
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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.