1985
DOI: 10.1016/0167-2789(85)90001-6
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Fractal basin boundaries

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Cited by 510 publications
(294 citation statements)
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“…7, where black dots represent the basin of the A > attractor. The dimension of the basin boundary is approximately 1.8, corresponding to an uncertainty exponent of +0.2 [78,79]. Now assume that the attractor A > corresponds to a better system performance so that it is the desirable attractor.…”
Section: Example 1: Controlling Fractal Basin Boundariesmentioning
confidence: 99%
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“…7, where black dots represent the basin of the A > attractor. The dimension of the basin boundary is approximately 1.8, corresponding to an uncertainty exponent of +0.2 [78,79]. Now assume that the attractor A > corresponds to a better system performance so that it is the desirable attractor.…”
Section: Example 1: Controlling Fractal Basin Boundariesmentioning
confidence: 99%
“…Here bỳ knowledgea we mean the Jacobian matrices J [note that f L can be calculated in terms of J ] and vector K in Eq. (79). A nonlinear time series of the process is enough to extract the necessary parameter perturbations to stabilize a chaotic trajectory around the unstable periodic orbit.…”
Section: Synchronization Of Low-dimensional Chaotic Systems By Controlmentioning
confidence: 99%
“…The presence of a homoclinic orbit causes that W ~ piles up against itself. This results in a sensitivity of 'eln e -~' type with respect to final states either in P0 or in its complement [5].…”
Section: Level Lines For the H4non Mappingmentioning
confidence: 99%
“…2-3 one can also infer properties of the basin boundary, especially about final state sensitivity [4,5]. In all cases shown, the unstable manifold W u of the saddle intersects a level line.…”
Section: Level Lines For the H4non Mappingmentioning
confidence: 99%
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