Bounds for bounded motion around a perturbed fixed point

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Damme, Ruud van and Valkering, Theo P. (1988) Bounds for bounded motion around a perturbed fixed point. Zeitschrift für Angewandte Mathematik und Physik, 39 (6). pp. 813-825. ISSN 0044-2275

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Abstract: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').
Item Type:Article
Copyright:© 1988 Springer
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/80010
Official URL:http://dx.doi.org/10.1007/BF00945120
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