Adding delay to the damping of a swing equation creates alternating stable and unstable Hopf bifurcations, with all new limit cycles initially growing toward larger delays.
On Norm-Based Estimations for Domains of Attraction in Nonlinear Time-Delay Systems
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abstract
For nonlinear time-delay systems, domains of attraction are rarely studied despite their importance for technological applications. The present paper provides methodological hints for the determination of an upper bound on the radius of attraction by numerical means. Thereby, the respective Banach space for initial functions has to be selected and primary initial functions have to be chosen. The latter are used in time-forward simulations to determine a first upper bound on the radius of attraction. Thereafter, this upper bound is refined by secondary initial functions, which result a posteriori from the preceding simulations. Additionally, a bifurcation analysis should be undertaken. This analysis results in a possible improvement of the previous estimation. An example of a time-delayed swing equation demonstrates the various aspects.
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math.DS 1years
2019 1verdicts
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Time Delay in the Swing Equation: A Variety of Bifurcations
Adding delay to the damping of a swing equation creates alternating stable and unstable Hopf bifurcations, with all new limit cycles initially growing toward larger delays.