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arXiv · 1502.01903

Multistable jittering in oscillators with pulsatile delayed feedback

Vladimir Klinshov·Leonhard Lücken·Dmitry Shchapin·Vladimir Nekorkin·Serhiy Yanchuk
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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.

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Vladimir Klinshov, Leonhard Lücken, Dmitry Shchapin, Vladimir Nekorkin, Serhiy Yanchuk. 2015-05-27. Multistable jittering in oscillators with pulsatile delayed feedback. https://doi.org/10.1103/physrevlett.114.178103

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