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Area of Science:

  • Nonlinear Dynamics
  • Computational Neuroscience
  • Theoretical Physics

Background:

  • Classical excitability describes systems with a nonlinear threshold response to perturbations from an equilibrium state.
  • Periodic orbits in dynamical systems typically exhibit predictable responses to perturbations.

Purpose of the Study:

  • To extend the concept of excitability to periodic orbits, introducing phase-sensitive excitability.
  • To investigate the role of perturbation timing on nonlinear threshold-like responses in periodic systems.
  • To analyze the impact of noise on phase-sensitive excitability and its associated dynamics.

Main Methods:

  • Utilized the FitzHugh-Nagumo system as a paradigmatic model for relaxation oscillations.
  • Analyzed the phase-sensitive nonlinear threshold-like response of these oscillations to perturbations.
  • Investigated the effect of noise on triggering excitability and its influence on the mean spiking rate.

Main Results:

  • Demonstrated that periodic orbits can exhibit phase-sensitive excitability, where responses depend on the phase of perturbation.
  • Identified the canard trajectory's nonlinear behavior as key to explaining the phase-sensitive response in the FitzHugh-Nagumo system.
  • Observed a non-monotone dependence of the mean spiking rate on noise level, resulting from competing excitation and response degradation effects.

Conclusions:

  • Phase-sensitive excitability is a novel form of excitable behavior occurring in periodic orbits.
  • The FitzHugh-Nagumo system exemplifies phase-sensitive excitability, linked to canard dynamics.
  • Noise influences phase-sensitive excitability, leading to complex, non-monotone firing rate behaviors.