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Parametric excitation and Hopf bifurcation analysis of a time delayed nonlinear feedback oscillator

Publication Type : Journal Article

Publisher : Springer India

Source : Springer India

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2020

Abstract : In this paper, an attempt has been made to understand the parametric excitation of a periodic orbit of nonlinear oscillator which can be a limit cycle, center or a slowly decaying center-type oscillation. For this a delay model is considered with nonlinear feedback oscillator defined in terms of Liénard oscillator description which can give rise to any one of the periodic orbits stated above. We have characterized the resonance and antiresonance behaviour for arbitrary nonlinear system from their stability and bifurcation analyses in reference to the standard delayed van der Pol system. An approximate analytical solution using Krylov–Bogoliubov (K–B) averaging method is utilised to recognize the sub-harmonic resonance and antiresonance, and average energy consumption per cycle

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