{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T20:32:45Z","timestamp":1759091565584},"reference-count":40,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2002,11]]},"abstract":"<jats:p> The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton's law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature difference across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one. Near the 1 : 2 spatial resonance in low Prandtl number fluids these effects open up intervals of Rayleigh number with no stable solutions in the form of steady convection or steadily traveling waves. Direct numerical simulations in two dimensions show that in such intervals the dynamics typically take the form of a nearly heteroclinic modulated traveling wave. This wave may be quasiperiodic or chaotic. <\/jats:p>","DOI":"10.1142\/s0218127402006047","type":"journal-article","created":{"date-parts":[[2002,12,19]],"date-time":"2002-12-19T09:46:50Z","timestamp":1040291210000},"page":"2501-2522","source":"Crossref","is-referenced-by-count":18,"title":["ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH\u2013B\u00c9NARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY"],"prefix":"10.1142","volume":"12","author":[{"given":"ISABEL","family":"MERCADER","sequence":"first","affiliation":[{"name":"Departament de F\u00edsica Aplicada,  Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JOANA","family":"PRAT","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tica Aplicada IV, Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"EDGAR","family":"KNOBLOCH","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics,  University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(87)90042-X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(88)90032-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/0149039"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112088001818"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1063\/1.868270"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-13319-4_15"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/4\/3\/005"},{"key":"rf8","first-page":"575","volume":"8","author":"Chossat P.","journal-title":"Dyn. 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