Multi-pulse phase resetting curve

Giri P. Krishnan,1, 2 Maxim Bazhenov,1 and Arkady Pikovsky2 1Department of Cell Biology and Neuroscience, University of California, Riverside CA, USA 2Department of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany (Dated: May 7, 2014) Abstract In this paper, we introduce and systematically study, in terms of phase response curves (PRC), the effect of a dual pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from a linear summation of phase advances from two small perturbations. We derive analytically a correction term, which generally appears for oscillators whose intrinsic dimensionality is greater than one. We demonstrate this effect in case of the Stuart-Landau model, and also in various higher dimensional neuronal model. The non-linear correction is found to be proportional to the square of the perturbation. This deviation from the superposition principle needs to be taken into account in studies of networks of pulse-coupled oscillators. Further, this deviation could be used for verification of oscillator models via a dual pulse excitation.