Phys. Rev. E 62, 4846–4849 (2000)Straight-line stabilizationReceived 13 January 2000; revised 12 May 2000; published in the issue dated October 2000 For finite-dimensional maps, an unstable orbit in a neighborhood of an unstable fixed point can be stabilized by adjusting parameters so that the orbit goes to the fixed point along the straight line connecting the orbit (at a given time) and the fixed point [Yang Ling, Liu Zengrong and Jian-min Mao, Phys. Rev. Lett. 84, 67 (2000)]. This is called straight-line stabilization. In this paper, we derive the expression for the region of stabilization, i.e., the region within which the straight-line stabilization method is valid. For two-dimensional maps, the parameter adjustments needed by the stabilization method are explicitly given for nine cases. Stabilization of unstable flows, with or without introducing a Poincaré map, is also investigated. © 2000 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.62.4846
DOI:
10.1103/PhysRevE.62.4846
PACS:
05.45.Gg, 05.45.Pq
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