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Sci. Comput."],"published-print":{"date-parts":[[2023,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear partial differential equations that characterizes Hopf bifurcation points. The flexibility and robustness of the method allows us to advance or delay a Hopf bifurcation to a target value of the bifurcation parameter, as well as controlling the oscillation frequency with respect to a parameter of the system or the shape of the domain on which solutions are defined. Numerical applications are presented in systems arising from biology and fluid dynamics, such as the FitzHugh\u2013Nagumo model, Ginzburg\u2013Landau equation, Rayleigh\u2013B\u00e9nard convection problem, and Navier\u2013Stokes equations, where the control of the location and oscillation frequency of periodic solutions is of high interest.<\/jats:p>","DOI":"10.1137\/22m1474448","type":"journal-article","created":{"date-parts":[[2023,6,28]],"date-time":"2023-06-28T17:13:46Z","timestamp":1687972426000},"page":"B390-B411","source":"Crossref","is-referenced-by-count":5,"title":["Optimization of Hopf Bifurcation Points"],"prefix":"10.1137","volume":"45","author":[{"given":"Nicolas","family":"Boull\u00e9","sequence":"first","affiliation":[{"name":"Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0EH, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1241-7060","authenticated-orcid":true,"given":"Patrick E.","family":"Farrell","sequence":"additional","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6872-3710","authenticated-orcid":true,"given":"Marie E.","family":"Rognes","sequence":"additional","affiliation":[{"name":"Department of Scientific Computing and Numerical Analysis, Simula Research Laboratory, Oslo, Norway, and Department of Mathematics, University of Bergen, Bergen, Norway."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,6,23]]},"reference":[{"key":"ref1","unstructured":"Software Used in \u201cOptimal Control of Hopf Bifurcations\n                      ,\u201d Firedrake-Zenodo, 2021, https:\/\/doi.org\/10.5281\/zenodo.5762538."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)90062-0"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-006-0017-y"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1145\/2566630"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.74.99"},{"key":"ref6","unstructured":"S. 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