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  • 1.
    Sah, S. M.
    et al.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Nanostructure Physics.
    Rand, R. H.
    Delay terms in the slow flow2016In: Journal of Applied Nonlinear Dynamics, ISSN 2164-6457, E-ISSN 2164-6473, Vol. 5, no 4, p. 471-484Article in journal (Refereed)
    Abstract [en]

    This work concerns the dynamics of nonlinear systems that are sub- jected to delayed self-feedback. Perturbation methods applied to such systems give rise to slow flows which characteristically contain delayed variables. We consider two approaches to analyzing Hopf bifurcations in such slow flows. In one approach, which we refer to as approach I, we follow many researchers in replacing the delayed variables in the slow flow with non-delayed variables, thereby reducing the DDE slow flow to an ODE. In a second approach, which we refer to as approach II, we keep the delayed variables in the slow flow. By comparing these two approaches we are able to assess the accuracy of making the simplifying assumption which replaces the DDE slow flow by an ODE. We apply this comparison to two examples, Duffing and van der Pol equations with self-feedback.

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