Multiple Scales and Energy Analysis of Coupled Rayleigh-Van Der Pol Oscillators With Time-Delayed Displacement and Velocity Feedback: Hopf Bifurcations and Amplitude Death

Abstract

In this paper, two classes of techniques, based on multiple scales perturbation analysis and the averaged energy (or Lyapunov function) method, are employed to investigate interesting nonlinear dynamical regimes in a system of coupled Rayleigh-Van der Pol oscillators with time-delayed displacement and velocity feedback. Such systems are currently of topical interest in many applications. The multiple scales

Bifurcation analysis of a forced delay equation for machine tool vibrations

“…Various techniques like the method of multiple scales [5][6][7][8][9][10], the Linstedt-Poincaré method [11], the combination of the method of multiple scales and the Linstedt-Poincaré method [12], harmonic balance method [13][14][15], method of averaging [16], semidiscretization [17], center manifold reduction [18,19] and normal forms [20] have been used to study delaydifferential equations.…”