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Area of Science:

  • Nonlinear Dynamics
  • Computational Neuroscience
  • Physics of Oscillators

Background:

  • Relaxation oscillators are fundamental in various scientific fields, including neuroscience.
  • Understanding oscillator response to external forcing is crucial for signal processing and biological modeling.
  • Previous studies often focused on forcing frequencies near or below the intrinsic frequency.

Purpose of the Study:

  • To investigate the behavior of a generic relaxation oscillator under high-frequency, unidirectional external forcing.
  • To explore the potential for 'overclocking' oscillators beyond their natural frequencies.
  • To analyze the stability and characteristics of resulting synchronous oscillations, particularly for neuroscience applications.

Main Methods:

  • Analysis of a generic relaxation oscillator model.
  • Application of moderately strong external forcing at frequencies significantly higher than the intrinsic frequency.
  • Analytical derivation of a phase map to explain observed phenomena.

Main Results:

  • Transition to high-frequency synchronous oscillations predominantly occurs via periodic solutions, with minimal chaotic regimes.
  • Achieved high-frequency oscillations exhibit large amplitudes, indicating potential practical significance.
  • The 1:1 synchronized solution loses stability at smaller frequency differences, a deviation from typical observations.

Conclusions:

  • Substantial 'overclocking' of relaxation oscillators is achievable with moderate external forcing.
  • The findings provide a mechanism for generating high-frequency, large-amplitude oscillations relevant to neuroscience.
  • Both excitatory and inhibitory inputs can effectively drive these high-frequency oscillations in neural models.