{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:11:16Z","timestamp":1761826276614,"version":"build-2065373602"},"reference-count":0,"publisher":"European Mathematical Society - EMS - Publishing House GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Port. Math."],"published-print":{"date-parts":[[2008,9,30]]},"abstract":"<jats:p>\n                    We study a vector-valued reaction-diffusion equation with Neumann boundary conditions\n                    <jats:inline-formula>\n                      <jats:tex-math>(u: [0,\u03c0] \u2192 \u211d^2<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    ). Unlike what is observed for scalar equations, where no heteroclinic connections involving periodic solutions occur, we find that steady-state\/Hopf and Hopf\/Hopf mode interactions produce heteroclinic solutions connecting at least one solution of standing wave type. This is achieved by restricting a problem with periodic boundary conditions and equivariant under\n                    <jats:inline-formula>\n                      <jats:tex-math>\\mathrm{O}(2)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    symmetry to a suitable fixed-point space.\n                  <\/jats:p>\n                  <jats:p>For completeness, we include a description of the solutions for Hopf bifurcation and mode interactions involving Hopf bifurcation, namely, steady-state\/Hopf and Hopf\/Hopf.<\/jats:p>","DOI":"10.4171\/pm\/1818","type":"journal-article","created":{"date-parts":[[2009,12,22]],"date-time":"2009-12-22T19:14:17Z","timestamp":1261509257000},"page":"373-385","source":"Crossref","is-referenced-by-count":0,"title":["Symmetry and bifurcation of periodic solutions in Neumann boundary value problems"],"prefix":"10.4171","volume":"65","author":[{"given":"Sofia B. S. D.","family":"Castro","sequence":"first","affiliation":[{"name":"Universidade do Porto, Portugal"}]}],"member":"2673","container-title":["Portugaliae Mathematica"],"original-title":[],"link":[{"URL":"http:\/\/www.ems-ph.org\/fulltext\/10.4171\/PM\/1818","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T12:06:50Z","timestamp":1761826010000},"score":1,"resource":{"primary":{"URL":"https:\/\/ems.press\/doi\/10.4171\/pm\/1818"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,30]]},"references-count":0,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.4171\/pm\/1818","relation":{},"ISSN":["0032-5155","1662-2758"],"issn-type":[{"type":"print","value":"0032-5155"},{"type":"electronic","value":"1662-2758"}],"subject":[],"published":{"date-parts":[[2008,9,30]]}}}