Optimization of Hopf bifurcation points
File(s)
Accepted version
Author(s)
Boullé, Nicolas
Farrell, Patrick E
Rognes, Marie E
Type
Journal Article
Abstract
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.
Date Issued
2023-06
Date Acceptance
2023-01-17
Citation
SIAM Journal on Scientific Computing, 2023, 45 (3), pp.B390-B411
ISSN
1064-8275
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Start Page
B390
End Page
B411
Journal / Book Title
SIAM Journal on Scientific Computing
Volume
45
Issue
3
Copyright Statement
© 2023 Society for Industrial and Applied Mathematics.
License URL
Identifier
http://dx.doi.org/10.1137/22m1474448
Publication Status
Published
Date Publish Online
2023-06-23