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Falling off a limit cycle using phase-agnostic stimuli: Definitions and conceptual framework.

Joshua Chang1, Varun Sridhar1, David Paydarfar1

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Chaos (Woodbury, N.Y.)
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Researchers found a way to stop biological oscillations at any point using specific stimuli. This phase-agnostic rhythm suppression uses a novel waveform to control oscillator behavior, applicable to complex biological systems.

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Area of Science:

  • * Mathematical biology
  • * Dynamical systems theory
  • * Biomedical engineering

Background:

  • * Oscillators with bistable limit cycle kinetics are fundamental in biological processes.
  • * Current methods to stop oscillations require precise phase-dependent stimuli.
  • * A phase-agnostic method for rhythm suppression remains a significant challenge.

Purpose of the Study:

  • * To investigate the possibility of creating stimuli that stop oscillations irrespective of the applied phase.
  • * To elucidate the mechanism underlying phase-agnostic rhythm suppression.
  • * To explore the relationship between stimulus properties and suppression efficiency.

Main Methods:

  • * Utilized a radial isochron clock model to simulate oscillator dynamics.
  • * Designed and tested various stimulus waveforms for their ability to suppress rhythm.
  • * Analyzed the phase-corralling and amplitude-suppression dynamics of the perturbation.

Main Results:

  • * Demonstrated the existence of stimulus waveforms capable of phase-agnostic rhythm suppression.
  • * Identified a mechanism involving phase corralling followed by driving the oscillator to a phase singularity.
  • * Characterized a library of waveforms with varying durations and suppression efficiencies.
  • * Found optimal stimulus energy depends on phase corralling rate and phaseless set configuration.

Conclusions:

  • * Phase-agnostic suppression of biological rhythms is achievable with specifically designed stimuli.
  • * The identified mechanism offers a novel approach to controlling oscillatory biological systems.
  • * Results suggest potential applications in regulating complex biological oscillators irrespective of their phase.