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Area of Science:

  • Dynamical Systems and Control Theory
  • Nonlinear Dynamics
  • Computational Neuroscience

Background:

  • Phase reduction is standard for weakly perturbed limit cycle oscillators.
  • Its accuracy decreases significantly with strong perturbations, necessitating amplitude dynamics consideration.

Purpose of the Study:

  • To develop and evaluate a phase-based control strategy for general limit cycle oscillators across weak and strong perturbation regimes.
  • To propose an optimal phase control strategy for strongly perturbed systems using an adaptive phase-amplitude reduced order model.

Main Methods:

  • Developed an adaptive phase-amplitude reduced order model.
  • Integrated dynamic programming for optimal phase control.
  • Applied the strategy to biologically relevant problems and compared it with existing algorithms.

Main Results:

  • The adaptive phase-amplitude reduction strategy effectively controls limit cycle oscillators under strong perturbations.
  • This method remains computationally tractable, unlike other strategies that fail with large inputs.
  • Demonstrated viability in biologically motivated scenarios.

Conclusions:

  • Accurate control of limit cycle oscillators, especially under strong perturbations, requires models that include amplitude dynamics.
  • The proposed adaptive phase-amplitude reduction offers a balance between model accuracy and computational tractability.
  • Careful selection of reduced order models is crucial for effective oscillator control.