Multipulse phase resetting curves.
In this paper, we introduce and study systematically, in terms of phase response curves, the effect of dual-pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from linear summation of phase advances resulting from two small perturbations. We analytically derive a correction term, which generally appears for oscillators whose intrinsic dimensionality is >1. The nonlinear correction term is found to be proportional to the square of the perturbation. We demonstrate this effect in the Stuart-Landau model and in various higher dimensional neuronal models. 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 in the verification of oscillator models via a dual-pulse excitation.
Department of Cell Biology and Neuroscience, University of California, Riverside, Riverside, California 92507, USA and Department of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.
Giri P
GP
Krishnan
Maxim
M
Bazhenov
Arkady
A
Pikovsky