WIAS Preprint No. 2100, (2015)

Multistable jittering in oscillators with pulsatile delayed feedback


  • Klinshov, Vladimir
  • Lücken, Leonhard
  • Shchapin, Dmitry
  • Nekorkin, Vladimir
  • Yanchuk, Serhiy

2010 Mathematics Subject Classification

  • 37G15 37N20 92B25

2008 Physics and Astronomy Classification Scheme

  • 87.19.ll, 05.45.Xt, 87.19.lr, 89.75.Kd


  • phase oscillator, delayed feedback, pulsatile feedback, jitter, degenerate bifurcation, PRC




Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in recent years. For such systems, we report a remarkable scenario of destabilization of a periodic regular spiking regime. At the bifurcation point numerous regimes with non-equal interspike intervals emerge. We show that the number of the emerging, so-called ``jittering'' regimes grows emphexponentially 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.

Appeared in

  • Phys. Rev. Lett., 114 (2015) pp. 178103/1--178103/5.

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