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Multipulse phase resetting curves.

Giri P Krishnan1, Maxim Bazhenov, Arkady Pikovsky

  • 1Department of Cell Biology and Neuroscience, University of California, Riverside, Riverside, California 92507, USA and Department of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.

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Summary
This summary is machine-generated.

Dual-pulse excitation of autonomous oscillators reveals nonlinear effects beyond simple summation. A correction term, dependent on perturbation squared, is derived and observed in models, impacting network studies and model verification.

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Area of Science:

  • Nonlinear Dynamics
  • Computational Neuroscience
  • Systems Biology

Background:

  • Autonomous oscillators are fundamental in various scientific fields.
  • Understanding oscillator responses to external stimuli is crucial for modeling complex systems.
  • Linear summation of phase advances is often assumed for small perturbations.

Purpose of the Study:

  • To systematically investigate the effect of dual-pulse excitation on autonomous oscillator dynamics.
  • To quantify deviations from linear summation of phase advances.
  • To introduce and analyze a nonlinear correction term.

Main Methods:

  • Analysis of phase response curves for dual-pulse excitation.
  • Analytical derivation of a correction term for phase advance summation.
  • Demonstration using the Stuart-Landau model and higher-dimensional neuronal models.

Main Results:

  • Identified deviations from linear summation of phase advances under dual-pulse excitation.
  • Derived a nonlinear correction term proportional to the square of the perturbation.
  • Observed this nonlinear effect in both the Stuart-Landau model and neuronal models.

Conclusions:

  • The superposition principle is violated in certain oscillator dynamics under dual-pulse excitation.
  • The derived nonlinear correction term is essential for accurate modeling of pulse-coupled oscillator networks.
  • Dual-pulse excitation can serve as a tool for verifying the accuracy of oscillator models.