A Consistent Definition of Phase Resetting Using Hilbert Transform

Figure 1

Phase resetting in response to a single inhibitory stimulus. (a) The unperturbed trajectory (continuous line) with an intrinsic firing period is perturbed at a stimulus time measured from an arbitrary voltage threshold (phase reference ). As a result, the new firing period is , which induces a permanent phase shift (resetting) in all subsequent cycles. (b) Phase space portrait of a stable limit cycle. The voltage (dashed) and slow variable (dotted) nullclines show a fixed point that leads to large amplitude, stable, limit cycle oscillations. The 20, equally spaced, solid dots along the limit cycle suggest that the figurative point moves at different speeds through the phase space. (c) A typical type 1 PRC for excitatory perturbations for a class I excitable cell has a unimodal shape. In this case, regardless of the stimulus phase, the next spike is always advanced (negative resetting) (d). For a class II excitable cell, the corresponding type 2 PRC is usually bimodal. The thick vertical arrow shows the timing of a brief current stimulus delivered at .

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