  A data-driven model identification strategy is developed for dynamical
systems near a supercritical Hopf bifurcation with nonautonomous inputs. This
strategy draws on phase-amplitude reduction techniques, leveraging an
analytical representation for the phase and amplitude response curves of the
Hopf normal form to infer system parameters. Fitting can be performed by
recording the system output during the relaxation to the stable limit cycle
after applying as few as two carefully timed pulse inputs. This strategy is
illustrated in two examples with relevance to circadian oscillations. In each
example, the proposed model identification strategy allows for the formulation,
solution, and implementation of a closed loop nonlinear optimal control
problem.
