Bounds for bounded motion around a perturbed fixed point

Ruud van Damme, Theo P. Valkering

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    We consider a dissipative map of the plane with a bounded perturbation term. This perturbation represents e.g. an extra time dependent term, a coupling to another system or noise. The unperturbed map has a spiral attracting fixed point. We derive an analytical/numerical method to determine the effect of the additional term on the phase portrait of the original map, as a function of the δ bound on the perturbation. This method yields a value δ c such that for δδ c the orbits about the attractor are certainly bounded. In that case we obtain a largest region in which all orbits remain bounded and a smallest region in which these bounded orbits are captured after some time (the analogue of 'basin' and 'attractor respectively').
    Original languageEnglish
    Pages (from-to)813-825
    JournalZeitschrift für angewandte Mathematik und Physik
    Issue number6
    Publication statusPublished - 1988


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