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Related Experiment Videos

Feedback control of canards.

Joseph Durham1, Jeff Moehlis

  • 1Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA. joey@engineering.ucsb.edu

Chaos (Woodbury, N.Y.)
|April 2, 2008
PubMed
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We developed a control method to precisely tune dynamical systems into the canard regime, enhancing sensitivity for parameter detection. This method, applied to the FitzHugh-Nagumo model, shows potential for improved sensor technology.

Area of Science:

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

Background:

  • Fast-slow dynamical systems exhibit complex behaviors near bifurcations.
  • The canard regime, a narrow parameter window, is crucial for understanding transitions between small and large amplitude oscillations.
  • Tuning systems to the canard regime is challenging due to its sensitivity.

Purpose of the Study:

  • To present a novel continuous feedback control mechanism for tuning fast-slow dynamical systems into the canard regime.
  • To demonstrate the application of this control strategy to the FitzHugh-Nagumo model for generating maximal canard orbits.
  • To investigate the impact of control parameter configuration and external noise on the system's behavior.

Main Methods:

Related Experiment Videos

  • Utilized a slow control variable for continuous feedback.
  • Applied the control mechanism to the FitzHugh-Nagumo model, a standard model for neuronal excitability.
  • Analyzed system dynamics under various control configurations and in the presence of noise.

    • Main Results:

    • Successfully tuned the FitzHugh-Nagumo model to achieve canard orbits.
    • Identified conditions leading to undesirable periodic or chaotic mixed-mode oscillations when the controller is improperly configured.
    • Demonstrated the robustness of the control mechanism against noise and its ability to enhance parameter sensitivity.

    Conclusions:

    • The proposed control mechanism effectively tunes fast-slow systems into the canard regime.
    • Proper controller configuration is essential to avoid chaotic behaviors.
    • Systems operating near the canard regime exhibit enhanced sensitivity, enabling the detection of minute parameter changes, with implications for sensor design.