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Multistable jittering in oscillators with pulsatile delayed feedback.

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Time-delayed feedback in oscillatory systems can destabilize regular spiking, leading to numerous "jittering" regimes with unequal intervals. This multijitter bifurcation robustly emerges and scales with delay, observed across models and experiments.

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Area of Science:

  • Dynamical systems theory
  • Computational neuroscience
  • Nonlinear dynamics

Background:

  • Oscillatory systems with time-delayed feedback are prevalent in science and engineering.
  • Understanding the stability and dynamics of these systems is crucial for various applications.
  • Previous research has focused on simpler feedback mechanisms.

Purpose of the Study:

  • To investigate the destabilization of periodic spiking regimes in systems with time-delayed pulsatile feedback.
  • To characterize the emergence and properties of novel dynamic regimes.
  • To demonstrate the robustness of observed phenomena across different models and experimental setups.

Main Methods:

  • Analysis of bifurcation phenomena in oscillatory systems.
  • Mathematical modeling of phase-reduced systems.
  • Simulation of the Hodgkin-Huxley neuron model.
  • Experimental validation using electronic circuits.

Main Results:

  • A novel scenario of periodic regular spiking regime destabilization was identified.
  • At the bifurcation point, numerous regimes with unequal interspike intervals (jittering regimes) emerge.
  • The number of jittering regimes increases exponentially with the time-delay value.
  • The multijitter bifurcation was observed robustly in phase-reduced models, a simulated neuron model, and an electronic circuit experiment.

Conclusions:

  • Time-delayed pulsatile feedback can lead to complex, robust destabilization of regular spiking.
  • The multijitter bifurcation represents a significant dynamical phenomenon with broad implications.
  • The findings are relevant for understanding neural oscillations, electronic circuit behavior, and other oscillatory systems.