{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T17:47:35Z","timestamp":1769017655786,"version":"3.49.0"},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,10]]},"abstract":"<jats:p> This paper presents methods to visualize bifurcations in flows of nonlinear dynamical systems, using the Lorenz '96 systems as examples. Three techniques are considered; the first two, density and max\/min diagrams, are analagous to the bifurcation diagrams used for maps, which indicate how the system's behavior changes with a control parameter. However the diagrams are generally harder to interpret than the corresponding diagrams of maps, due to the continuous nature of the flow. The third technique takes an alternative approach: by calculating the power spectrum at each value of the control parameter, a plot is produced which clearly shows the changes between periodic, quasi-periodic, and chaotic states, and reveals structure not shown by the other methods. <\/jats:p>","DOI":"10.1142\/s0218127403008387","type":"journal-article","created":{"date-parts":[[2003,12,1]],"date-time":"2003-12-01T04:06:11Z","timestamp":1070251571000},"page":"3015-3027","source":"Crossref","is-referenced-by-count":31,"title":["VISUALIZING BIFURCATIONS IN HIGH DIMENSIONAL SYSTEMS: THE SPECTRAL BIFURCATION DIAGRAM"],"prefix":"10.1142","volume":"13","author":[{"given":"DAVID","family":"ORRELL","sequence":"first","affiliation":[{"name":"Institute for Systems Biology,  1441 N 34th Street, Seattle, WA 98103, USA"},{"name":"Mathematical Institute, University of Oxford,  24\u201329 St Giles', Oxford OX1 3LB, UK"}]},{"given":"LEONARD A.","family":"SMITH","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford,  24\u201329 St Giles', Oxford OX1 3LB, UK"},{"name":"Centre for the Analysis of Time Series,  Department of Statistics, London School of Economics, Houghton Street,  London WC2A 2AE, UK"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"crossref","DOI":"10.1007\/b97589","volume-title":"Chaos: An Introduction to Nonlinear Dynamical Systems","author":"Alligood K. T.","year":"1996"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(2000)057<2859:TROOCI>2.0.CO;2"},{"key":"rf5","volume-title":"Predictability","author":"Lorenz E.","year":"1996"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1109\/20.305647"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.5194\/npg-8-357-2001"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1034\/j.1600-0870.2002.01389.x"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(2003)060<2219:MEAPOD>2.0.CO;2"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127403008387","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:15:38Z","timestamp":1565122538000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127403008387"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":8,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,10]]}},"alternative-id":["10.1142\/S0218127403008387"],"URL":"https:\/\/doi.org\/10.1142\/s0218127403008387","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}