PhasenResponseKurve

PhasenResponseKurve, commonly referred to in English as the Phase Response Curve (PRC), is a function that describes how the phase of an oscillatory system changes in response to a perturbation delivered at a particular point in its cycle. It applies to a wide range of self-sustained oscillators, including neural firing, cardiac pacemaker cells, circadian clocks, and other rhythmic processes.

In formal terms, for a periodic oscillator with period T, a perturbation applied at phase φ (measured from 0 to 2π or from 0 to T) induces a phase shift Δφ. The PhasenResponseKurve is the mapping φ → Δφ, optionally normalized to a unit interval (0 to 1) or to a shift within one cycle. The curve is typically constructed by delivering brief inputs and measuring the resulting advancement or delay of the next event in the cycle, such as a spike or peak.

Two broad classes are commonly distinguished. Type I PRCs show only phase advances or only delays when perturbed, often associated with near-threshold excitability or certain types of perturbations. Type II PRCs contain regions of both positive and negative Δφ, indicating that perturbations can either advance or delay the cycle depending on the phase of application; this is common in systems with inhibitory interactions or with resonant dynamics.

Measurement and analysis may involve experimental perturbations at different phases, phase mapping of the oscillator’s response, or mathematical phase reduction techniques for limit-cycle models. The PhasenResponseKurve is a key tool for understanding synchronization, entrainment to external cues, and the collective dynamics of coupled oscillators in biology and engineering. It also informs how inputs influence timing variability and robustness of rhythmic systems.