Effects of time-delayed feedback on the properties of self-sustained oscillators

S. Risau-Gusman
Phys. Rev. E 94, 042212 – Published 18 October 2016

Abstract

Most self-sustained oscillations in biological systems and in technical applications are based on a feedback loop, and it is usually important to know how they will react when an external oscillatory force is applied. Here we investigate the effects that the introduction of a time delay in the feedback can have in the entrainment properties of self-sustained oscillators. To do this, we derive analytic expressions for the periodic trajectories and their asymptotic stability, for a generic external oscillatory force. This allows us to show that, for large quality factors, the resonance frequency does not depend on the feedback delay. When the external force is harmonic, it is shown that the largest entrainment range does not correspond to the time delay that gives the maximal response of the unforced oscillator. In fact, that delay gives the shortest entrainment range.

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  • Received 31 May 2016
  • Revised 22 September 2016

DOI:https://doi.org/10.1103/PhysRevE.94.042212

©2016 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear Dynamics

Authors & Affiliations

S. Risau-Gusman

  • Centro Atómico Bariloche, 8400 S. C. de Bariloche, Argentina and Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina

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Issue

Vol. 94, Iss. 4 — October 2016

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