Multistable jittering in oscillators with pulsatile delayed feedback
Abstract
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a periodic regular spiking regime. In the bifurcation point numerous regimes with non-equal interspike intervals emerge simultaneously. We show that this bifurcation is triggered by the steepness of the oscillator's phase resetting curve and that the number of the emerging, so-called "jittering" regimes grows exponentially with the delay value. Although this appears as highly degenerate from a dynamical systems viewpoint, the "multi-jitter" bifurcation occurs robustly in a large class of systems. We observe it not only in a paradigmatic phase-reduced model, but also in a simulated Hodgkin-Huxley neuron model and in an experiment with an electronic circuit.
Cite
@article{arxiv.1502.01903,
title = {Multistable jittering in oscillators with pulsatile delayed feedback},
author = {Vladimir Klinshov and Leonhard Lücken and Dmitry Shchapin and Vladimir Nekorkin and Serhiy Yanchuk},
journal= {arXiv preprint arXiv:1502.01903},
year = {2015}
}