Optimization of Hopf bifurcation points
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 bifurcat...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Society for Industrial and Applied Mathematics
2023
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| _version_ | 1797110197027602432 |
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| author | Boullé, N Farrell, PE Rognes, ME |
| author_facet | Boullé, N Farrell, PE Rognes, ME |
| author_sort | Boullé, N |
| collection | OXFORD |
| description | 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–Nagumo model, Ginzburg–Landau equation, Rayleigh–Bénard convection problem, and Navier–Stokes equations, where the control of the location and oscillation frequency of periodic solutions is of high interest. |
| first_indexed | 2024-03-07T07:51:11Z |
| format | Journal article |
| id | oxford-uuid:98eab844-4fb6-43d0-a34c-a8e21a65736a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:51:11Z |
| publishDate | 2023 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:98eab844-4fb6-43d0-a34c-a8e21a65736a2023-07-13T08:24:59ZOptimization of Hopf bifurcation pointsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:98eab844-4fb6-43d0-a34c-a8e21a65736aEnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2023Boullé, NFarrell, PERognes, MEWe 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–Nagumo model, Ginzburg–Landau equation, Rayleigh–Bénard convection problem, and Navier–Stokes equations, where the control of the location and oscillation frequency of periodic solutions is of high interest. |
| spellingShingle | Boullé, N Farrell, PE Rognes, ME Optimization of Hopf bifurcation points |
| title | Optimization of Hopf bifurcation points |
| title_full | Optimization of Hopf bifurcation points |
| title_fullStr | Optimization of Hopf bifurcation points |
| title_full_unstemmed | Optimization of Hopf bifurcation points |
| title_short | Optimization of Hopf bifurcation points |
| title_sort | optimization of hopf bifurcation points |
| work_keys_str_mv | AT boullen optimizationofhopfbifurcationpoints AT farrellpe optimizationofhopfbifurcationpoints AT rognesme optimizationofhopfbifurcationpoints |