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Controlling birhythmicity in a self-sustained oscillator by time-delayed feedback

Pushpita Ghosh1, Shrabani Sen1, Syed Shahed Riaz2, and Deb Shankar Ray1,*

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700 032, India
  • 2Department of Chemistry, Belur Ramakrishna Mission Vidyamandira, Howrah, 711202, India

  • *pcdsr@iacs.res.in
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Phys. Rev. E 83, 036205 – Published 17 March, 2011

DOI: https://doi.org/10.1103/PhysRevE.83.036205

Abstract

Time-delayed feedback is a practical method for controlling various nonlinear dynamical systems. We consider its influence on the dynamics of a multicycle van der Pol oscillator that is birhythmic in nature. It has been shown that depending on the strength of delay the bifurcation space can be divided into two subspaces for which the dynamical response of the system is generically distinct. We observe an interesting collapse and revival of birhythmicity with the variation of the delay time. Depending on the parameter space the system also exhibits a transition between birhythmicity and monorhythmic behavior. Our analysis of amplitude equation corroborates with the results obtained by numerical simulation of the dynamics.

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Phys. Rev. E 83, 036205– Published 17 March, 2011
  • Received 20 August 2010

©2011 American Physical Society

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