{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T07:38:33Z","timestamp":1648798713279},"reference-count":36,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,8]]},"abstract":"<jats:p> We study the effects of thermal noise in a stochastic, Langevin formulation, of a spatio-temporal pattern-forming Partial Differential Equation (PDE) model with circular domain. Modification of a recently developed numerical integration scheme reveals that the pattern-forming model exhibits, in the presence of noise, a greater tendency towards dynamic states and towards intermittent patterns in which ordered states appear randomly, preceded and succeeded by disorganized states. In order to gain additional insight, we focus on a region of parameter space where the patterns of the deterministic system arise from the steady-state interaction of two pairs of modes with wave numbers in a 1:2 ratio. Analysis of the associated stochastic normal form equations allows us to explain the underlying bifurcations of the noise-induced patterns, some of which had only been observed, until now, in laboratory experiments. <\/jats:p>","DOI":"10.1142\/s0218127407018749","type":"journal-article","created":{"date-parts":[[2007,9,24]],"date-time":"2007-09-24T10:16:13Z","timestamp":1190628973000},"page":"2765-2779","source":"Crossref","is-referenced-by-count":5,"title":["NOISE-INDUCED INTERMITTENCY IN CELLULAR PATTERN-FORMING SYSTEMS"],"prefix":"10.1142","volume":"17","author":[{"given":"SCOTT","family":"GASNER","sequence":"first","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PETER","family":"BLOMGREN","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANTONIO","family":"PALACIOS","sequence":"additional","affiliation":[{"name":"Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0026-0800(70)90038-8"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(88)90032-2"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971538"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.72.036701"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1063\/1.1848311"},{"key":"rf6","volume-title":"Pattern Formation in Biology, Vision and Dynamics","author":"Carbone A.","year":"1998"},{"key":"rf7","volume-title":"New Trends in Nonlinear Dynamics and Pattern Forming Phenomena","author":"Chat\u00e9 H.","year":"1990"},{"key":"rf8","first-page":"60","volume":"43","author":"Crank J.","journal-title":"Proc. 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