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Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport. <\/jats:p>","DOI":"10.1142\/s0218127416300366","type":"journal-article","created":{"date-parts":[[2016,12,29]],"date-time":"2016-12-29T04:22:06Z","timestamp":1482985326000},"page":"1630036","source":"Crossref","is-referenced-by-count":26,"title":["Lagrangian Descriptors for Stochastic Differential Equations: A Tool for Revealing the Phase Portrait of Stochastic Dynamical Systems"],"prefix":"10.1142","volume":"26","author":[{"given":"Francisco","family":"Balibrea-Iniesta","sequence":"first","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas, CSIC-UAM-UC3M-UCM, C\/Nicol\u00e1s Cabrera 15, Campus de Cantoblanco UAM, Madrid 28049, Spain"}]},{"given":"Carlos","family":"Lopesino","sequence":"additional","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas, CSIC-UAM-UC3M-UCM, C\/Nicol\u00e1s Cabrera 15, Campus de Cantoblanco UAM, Madrid 28049, Spain"}]},{"given":"Stephen","family":"Wiggins","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol, Bristol BS8 1TW, UK"}]},{"given":"Ana M.","family":"Mancho","sequence":"additional","affiliation":[{"name":"Instituto de Ciencias Matem\u00e1ticas, CSIC-UAM-UC3M-UCM, C\/Nicol\u00e1s Cabrera 15, Campus de Cantoblanco UAM, Madrid 28049, Spain"}]}],"member":"219","published-online":{"date-parts":[[2016,12,29]]},"reference":[{"key":"S0218127416300366BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12878-7"},{"key":"S0218127416300366BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01845701"},{"key":"S0218127416300366BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.06.016"},{"key":"S0218127416300366BIB005","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.148301"},{"key":"S0218127416300366BIB006","doi-asserted-by":"publisher","DOI":"10.1039\/C5CP06624G"},{"key":"S0218127416300366BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00258-4"},{"key":"S0218127416300366BIB008","doi-asserted-by":"publisher","DOI":"10.1175\/JAS-D-11-0142.1"},{"key":"S0218127416300366BIB009","doi-asserted-by":"publisher","DOI":"10.1175\/JAS-D-12-0274.1"},{"key":"S0218127416300366BIB010","volume-title":"An Introduction to Stochastic Dynamics","author":"Duan J.","year":"2015"},{"key":"S0218127416300366BIB011","doi-asserted-by":"publisher","DOI":"10.5194\/npg-22-701-2015"},{"key":"S0218127416300366BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.marpolbul.2016.08.018"},{"key":"S0218127416300366BIB014","doi-asserted-by":"publisher","DOI":"10.5194\/npg-9-237-2002"},{"key":"S0218127416300366BIB015","doi-asserted-by":"publisher","DOI":"10.1039\/C6CP02532C"},{"key":"S0218127416300366BIB016","doi-asserted-by":"publisher","DOI":"10.1021\/acs.jpcb.5b09003"},{"key":"S0218127416300366BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12616-5"},{"key":"S0218127416300366BIB018","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/176"},{"key":"S0218127416300366BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2015.02.022"},{"key":"S0218127416300366BIB020","author":"Lopesino C.","year":"2017","journal-title":"Int. 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