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Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback.

Sue Ann Campbell1, Jacques Belair, Toru Ohira

  • 1Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montreal, CanadaDepartment of Applied Mathematics, University of Waterloo, Waterloo, CanadaCentre de Recherches Mathematiques, Universite de Montreal, Montreal, CanadaCentre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montreal, CanadaCentre de Recherches Mathematiques and Department de Mathematiques et de Statistique, Universite de Montreal, Montreal, CanadaSony Computer Science Laboratory, Inc., Tokyo, JapanDepartment of Neurology and Committee on Neurobiology, The University of Chicago Hospitals, MC2030, 5841 South Maryland, Chicago, Illinois 60637Centre for Nonlinear Dynamics in Physiology and Medicine, McGill University, Montreal, Canada.

Chaos (Woodbury, N.Y.)
|December 1, 1995
PubMed
Summary

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Complex dynamics like limit cycles and multistability arise in a damped harmonic oscillator with delayed negative feedback. This finding is crucial for understanding mechanical and neuromechanical feedback systems.

Area of Science:

  • Mechanical Engineering
  • Nonlinear Dynamics
  • Control Systems

Background:

  • Delayed feedback is common in mechanical and neuromechanical systems.
  • Understanding complex dynamics in such systems is essential for design and stability analysis.

Purpose of the Study:

  • To investigate the complex dynamics, including limit cycles, two-tori, and multistability, in a damped harmonic oscillator with delayed negative feedback.
  • To establish this model as a prototype for systems with delayed feedback.

Main Methods:

  • Center manifold reduction.
  • Numerical calculations.

Main Results:

  • Demonstrated the presence of limit cycles.
  • Identified two-tori and multistability.

Related Experiment Videos

  • Showcased complex dynamics in a plausible mechanical model with delayed feedback.

    • Conclusions:

    • Delayed negative feedback can induce complex dynamics in mechanical systems.
    • The damped harmonic oscillator with delayed feedback serves as a key model for studying such phenomena.
    • Findings are applicable to a wide range of mechanical and neuromechanical feedback systems.