Delay coordinate embedding attractor reconstruction of the strange nonchaotic dynamics of the pulsating star KIC 5520878
Periodically driven damped nonlinear systems can exhibit complex dynamics characterized by strange chaotic attractors, where strange refers to the fractal geometry of the attractor and chaotic refers to the exponential sensitivity of orbits on the attractor. Quasiperiodically driven systems forced by incommensurate frequencies are natural extensions of periodically driven ones and are phenomenologically richer. In addition to periodic or quasiperiodic motion, they can exhibit chaotic or nonchaotic motion on strange attractors. Although quasiperiodic forcing is not necessary for strange nonchaotic dynamics (e.g., the period doubling accumulation point of a period doubling cascade), if quasiperiodic driving is not present, strange nonchaotic attractors are typically not robust and not expected to occur naturally because they exist only when the system is carefully tuned to a precise critical parameter value. On the other hand, it was shown in the paper of Grebogi et al. that SNAs can be robust when the system is quasiperiodically driven. The first experiment to demonstrate a robust strange nonchaotic attractor involved the buckling of a magnetoelastic ribbon driven quasiperiodically by two incommensurate frequencies in the golden ratio.[4] Strange nonchaotic attractors have been robustly observed in laboratory experiments involving magnetoelastic ribbons, electrochemical cells, electronic circuits, and a neon glow discharge. In 2015, strange nonchaotic dynamics were identified for the pulsating RR Lyrae variable KIC 5520878, as well as three similar stars observed by the Kepler space telescope, which oscillate in two frequency modes that are nearly in the golden ratio.[5][6][7][8]
Referencesedit
^ abLluís Alsedà (March 8, 2007). "On the definition of Strange Nonchaotic Attractor" (PDF). Retrieved 2014-05-07.
^Grebogi, Celso; Ott, Edward; Pelikan, Steven; Yorke, James A. (1984). "Strange attractors that are not chaotic". Physica D: Nonlinear Phenomena. 13 (1–2). Elsevier BV: 261–268. doi:10.1016/0167-2789(84)90282-3. ISSN 0167-2789.
^Gopal, R.; Venkatesan, A.; Lakshmanan, M. (2013). "Applicability of 0-1 Test for Strange Nonchaotic Attractors". Chaos: An Interdisciplinary Journal of Nonlinear Science. 23 (2): 023123. arXiv:1303.0169. Bibcode:2013Chaos..23b3123G. doi:10.1063/1.4808254. PMID 23822488.
^Ditto, W. L.; Spano, M. L.; Savage, H. T.; Rauseo, S. N.; Heagy, J.; Ott, E. (1990-07-30). "Experimental observation of a strange nonchaotic attractor". Physical Review Letters. 65 (5). American Physical Society (APS): 533–536. doi:10.1103/physrevlett.65.533. ISSN 0031-9007.
^Lindner, John F.; Kohar, Vivek; Kia, Behnam; Hippke, Michael; Learned, John G.; Ditto, William L. (2015-02-03). "Strange Nonchaotic Stars". Physical Review Letters. 114 (5). American Physical Society (APS): 054101. arXiv:1501.01747. doi:10.1103/physrevlett.114.054101. ISSN 0031-9007.
strange, nonchaotic, attractor, mathematics, strange, nonchaotic, attractor, form, attractor, which, while, converging, limit, strange, because, piecewise, differentiable, also, chaotic, that, lyapunov, exponents, positive, snas, were, introduced, topic, study. In mathematics a strange nonchaotic attractor SNA is a form of attractor which while converging to a limit is strange because it is not piecewise differentiable and also non chaotic in that its Lyapunov exponents are non positive 1 SNAs were introduced as a topic of study by Grebogi et al in 1984 1 2 SNAs can be distinguished from periodic quasiperiodic and chaotic attractors using the 0 1 test for chaos 3 source source source source source source Delay coordinate embedding attractor reconstruction of the strange nonchaotic dynamics of the pulsating star KIC 5520878Periodically driven damped nonlinear systems can exhibit complex dynamics characterized by strange chaotic attractors where strange refers to the fractal geometry of the attractor and chaotic refers to the exponential sensitivity of orbits on the attractor Quasiperiodically driven systems forced by incommensurate frequencies are natural extensions of periodically driven ones and are phenomenologically richer In addition to periodic or quasiperiodic motion they can exhibit chaotic or nonchaotic motion on strange attractors Although quasiperiodic forcing is not necessary for strange nonchaotic dynamics e g the period doubling accumulation point of a period doubling cascade if quasiperiodic driving is not present strange nonchaotic attractors are typically not robust and not expected to occur naturally because they exist only when the system is carefully tuned to a precise critical parameter value On the other hand it was shown in the paper of Grebogi et al that SNAs can be robust when the system is quasiperiodically driven The first experiment to demonstrate a robust strange nonchaotic attractor involved the buckling of a magnetoelastic ribbon driven quasiperiodically by two incommensurate frequencies in the golden ratio 4 Strange nonchaotic attractors have been robustly observed in laboratory experiments involving magnetoelastic ribbons electrochemical cells electronic circuits and a neon glow discharge In 2015 strange nonchaotic dynamics were identified for the pulsating RR Lyrae variable KIC 5520878 as well as three similar stars observed by the Kepler space telescope which oscillate in two frequency modes that are nearly in the golden ratio 5 6 7 8 References edit a b Lluis Alseda March 8 2007 On the definition of Strange Nonchaotic Attractor PDF Retrieved 2014 05 07 Grebogi Celso Ott Edward Pelikan Steven Yorke James A 1984 Strange attractors that are not chaotic Physica D Nonlinear Phenomena 13 1 2 Elsevier BV 261 268 doi 10 1016 0167 2789 84 90282 3 ISSN 0167 2789 Gopal R Venkatesan A Lakshmanan M 2013 Applicability of 0 1 Test for Strange Nonchaotic Attractors Chaos An Interdisciplinary Journal of Nonlinear Science 23 2 023123 arXiv 1303 0169 Bibcode 2013Chaos 23b3123G doi 10 1063 1 4808254 PMID 23822488 Ditto W L Spano M L Savage H T Rauseo S N Heagy J Ott E 1990 07 30 Experimental observation of a strange nonchaotic attractor Physical Review Letters 65 5 American Physical Society APS 533 536 doi 10 1103 physrevlett 65 533 ISSN 0031 9007 Lindner John F Kohar Vivek Kia Behnam Hippke Michael Learned John G Ditto William L 2015 02 03 Strange Nonchaotic Stars Physical Review Letters 114 5 American Physical Society APS 054101 arXiv 1501 01747 doi 10 1103 physrevlett 114 054101 ISSN 0031 9007 Applied Chaos Laboratory appliedchaoslab phys hawaii edu Clara Moskowitz 2015 02 09 Strange Stars Pulsate According to the Golden Ratio Scientific American Retrieved 2020 01 11 Lindner John F Kohar Vivek Kia Behnam Hippke Michael Learned John G Ditto William L 2015 Stars That Act Irrational Physical Review Letters 114 5 054101 arXiv 1501 01747 Bibcode 2015PhRvL 114e4101L doi 10 1103 PhysRevLett 114 054101 PMID 25699444 nbsp This mathematics related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Strange nonchaotic attractor amp oldid 1186093467, wikipedia, wiki, book, books, library,
