On the nonlinear features of time-delayed feedback oscillators
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An alternative approach to using phase plots, bifurcation diagrams, or Fourier analysis for characterizing the various responses displayed by time-delayed feedback oscillators of both autonomous and non-autonomous types is presented. The alternative employs the fundamental notion of instantaneous frequency to describe characteristics innate to periodic, quasi-periodic and chaotic motions in response to varying positive feedback and forcing parameters. Simultaneous periodicity-modal aberrations are seen to precede the birth of new modes, which explicitly signifies the inception of bifurcation. Modes thus defined in the context of instantaneous frequency are obtained using a separation scheme referred to as the empirical mode decomposition and thus, by definition, they are also an orthogonal set of intrinsic monocomponents each retaining the physical features inherent to the motions being studied. © 2003 Elsevier B.V. All rights reserved.
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