Abstract
The asymptotic behaviour of the phase-resetting map for generic one-parameter families of kicked planar oscillators, near the transition from degree 1, is studied. There are five cases. In each, the phase-resetting map is found to be already non-monotone before the transition, explaining experimental results like those of Jalife and Antzelevitch and Glass et al. Semi-universal forms are found in each case for the behaviour near the transition. The results extend to a large class of higher-dimensional oscillators.
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