Multistable jittering in oscillators with pulsatile delayed feedback

TL;DR

This paper investigates a novel bifurcation phenomenon called 'multi-jitter' in oscillators with delayed pulsatile feedback, showing it leads to multiple coexisting jittering regimes and occurs robustly across models and experiments.

Contribution

It introduces the concept of multi-jitter bifurcation, demonstrating its robustness and exponential growth with delay in various oscillator models and experimental setups.

Findings

Multi-jitter bifurcation causes multiple jittering regimes.

The bifurcation is triggered by the steepness of the phase resetting curve.

Number of regimes grows exponentially with delay.

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.